Question

question
∠1 and ∠2 are supplementary angles. if ( mangle1=(x - 19)^{circ}) and ( mangle2=(x + 23)^{circ}), 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 \(m\angle1=(x - 19)^{\circ}\) and \(m\angle2=(x + 23)^{\circ}\) into the equation: \((x - 19)+(x + 23)=180\).

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

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

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

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

Answer:

\(111^{\circ}\)