Question

∠1 and ∠2 are supplementary angles. if m∠1=(x + 15)° and m∠2=(4x + 5)°, then find the measure of ∠2.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(x + 15)^{\circ}\) and \(m\angle2=(4x + 5)^{\circ}\) into the equation: \((x + 15)+(4x + 5)=180\).

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

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

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

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

Answer:

\(133^{\circ}\)