Question

1. in the figure, ( mangle4 = 118^{circ} ). find each angle measure. justify each step.

a. ( mangle8 )
b. ( mangle7 )

1. proof write a paragraph

Explanation:

Step1: Find \(m\angle8\)

Since \(\angle4\) and \(\angle8\) are corresponding angles (parallel lines cut by a transversal), and corresponding angles are congruent.
\(m\angle8 = m\angle4\)

Step2: Find \(m\angle7\)

Since \(\angle7\) and \(\angle8\) are supplementary angles (\(\angle7+\angle8 = 180^{\circ}\) as they form a linear pair).
\(m\angle7=180^{\circ}-m\angle8\)

Answer:

a. \(m\angle8 = 118^{\circ}\) (Corresponding angles postulate)
b. \(m\angle7=180^{\circ}- 118^{\circ}=62^{\circ}\) (Linear pair postulate)