Question

find the measure of ∠1 and ∠2. justify the answer

Explanation:

Step1: Identify vertical - angle relationship

The angle of \(121^{\circ}\) and \(\angle1\) are vertical angles. Vertical angles are equal.
So, \(\angle1 = 121^{\circ}\)

Step2: Use linear - pair relationship

\(\angle1\) and \(\angle2\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\).
Let \(\angle2=x\), then \(121^{\circ}+x = 180^{\circ}\), so \(x=\angle2=180^{\circ}- 121^{\circ}=59^{\circ}\)

Answer:

\(\angle1 = 121^{\circ}\), \(\angle2 = 59^{\circ}\)