Question

a) name the angle relationship. b) congruent or supplementary c) solve for x. x + 92 x + 112

Explanation:

Step1: Identify angle - relationship

The angles are same - side interior angles.

Step2: Determine congruent or supplementary

Same - side interior angles formed by parallel lines are supplementary. So, \((x + 92)+(x + 112)=180\).

Step3: Simplify the equation

Combine like terms: \(x+x+92 + 112=180\), which gives \(2x+204 = 180\).

Step4: Solve for x

Subtract 204 from both sides: \(2x=180 - 204=- 24\). Then divide both sides by 2: \(x=-12\).

Answer:

A. Same - side interior angles
B. Supplementary
C. \(x=-12\)