Question

∠1 and ∠2 are supplementary angles. if (mangle1=(x - 23)^{circ}) and (mangle2=(x - 17)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(x - 23)^{\circ}\) and \(m\angle2=(x - 17)^{\circ}\) into the equation: \((x - 23)+(x - 17)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(x+x-23 - 17 = 180\), which simplifies to \(2x-40 = 180\).

Step3: Solve for \(x\)

Add 40 to both sides of the equation: \(2x-40 + 40=180 + 40\), so \(2x=220\).
Divide both sides by 2: \(x = 110\).

Step4: Find the measure of \(\angle2\)

Substitute \(x = 110\) into the expression for \(m\angle2\): \(m\angle2=(x - 17)^{\circ}=(110 - 17)^{\circ}=93^{\circ}\).

Answer:

\(93^{\circ}\)