Question

question
∠1 and ∠2 are supplementary angles. if m∠1=(2x + 27)° and m∠2=(2x - 3)°, then find the measure of ∠2.

Explanation:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180^{\circ}$.
So, $(2x + 27)+(2x - 3)=180$.

Step2: Simplify the left - hand side

Combine like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like li…

Answer:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180^{\circ}$.
So, $(2x + 27)+(2x - 3)=180$.

Step2: Simplify the left - hand side

Combine like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like 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like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like like li…