Question

∠1 and ∠2 are supplementary angles. if (mangle1=(x + 15)^{circ}) and (mangle2=(4x + 5)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
\((x + 15)+(4x + 5)=180\)

Step2: Combine like - terms

\(x+4x+15 + 5=180\), which simplifies to \(5x+20 = 180\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(5x=180 - 20=160\). Then divide both sides by 5: \(x=\frac{160}{5}=32\).

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

Substitute \(x = 32\) into the expression for \(m\angle2\). \(m\angle2=(4x + 5)^{\circ}=(4\times32+5)^{\circ}=(128 + 5)^{\circ}=133^{\circ}\).

Answer:

\(133^{\circ}\)