Question

∠1 and ∠2 are supplementary angles. if ( m∠1=(x - 19)^{circ} ) and ( m∠2=(x + 23)^{circ} ), then find the measure of ∠2.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \((x - 19)+(x + 23)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+x-19 + 23=180\), which gives \(2x+4 = 180\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(2x=180 - 4=176\). Then divide by \(2\): \(x=\frac{176}{2}=88\).

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

Substitute \(x = 88\) into \(m\angle2=(x + 23)^{\circ}\). So, \(m\angle2=(88+23)^{\circ}=111^{\circ}\).

Answer:

\(111\)