Question

∠1 and ∠2 are supplementary angles. if m∠1=(5x−27)° and m∠2=(6x−24)°, then find the measure of ∠2.

Explanation:

Step1: Use the supplementary angles property

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute the given expressions: \((5x - 27)+(6x - 24)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(5x+6x-27 - 24=180\), which is \(11x-51 = 180\).

Step3: Solve for \(x\)

Add \(51\) to both sides: \(11x=180 + 51\), so \(11x=231\).
Divide both sides by \(11\): \(x=\frac{231}{11}=21\).

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

Substitute \(x = 21\) into \(m\angle2=(6x - 24)^{\circ}\).
\(m\angle2=(6\times21-24)^{\circ}=(126 - 24)^{\circ}=102^{\circ}\).

Answer:

\(102^{\circ}\)