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: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(2x + 27)^{\circ}\) and \(m\angle2=(2x - 3)^{\circ}\) into the equation: \((2x + 27)+(2x - 3)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+2x + 27-3=180\), which simplifies to \(4x+24 = 180\).

Step3: Solve for \(x\)

Subtract 24 from both sides: \(4x=180 - 24\), so \(4x=156\).
Then divide both sides by 4: \(x=\frac{156}{4}=39\).

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

Substitute \(x = 39\) into the expression for \(m\angle2\): \(m\angle2=(2x - 3)^{\circ}=(2\times39-3)^{\circ}\).
First, calculate \(2\times39 = 78\), then \(78-3=75^{\circ}\).

Answer:

\(75^{\circ}\)