Question

consider the figure shown below. find the values of \\( \angle 1 \\) and \\( \angle 2 \\) for the given figures and complete the table accordingly. figure 3 figure angle 1 angle 2 figure 3

Explanation:

Step1: Find the measure of ∠2

Use the linear - pair property. If two angles form a linear pair, their sum is \(180^{\circ}\).
\(\angle2 + 157^{\circ}=180^{\circ}\)
\(\angle2=180^{\circ}- 157^{\circ}=23^{\circ}\)

Step2: Assume lines \(m\) and \(n\) are parallel and use the consecutive - interior angles property

If \(m\parallel n\), then \(\angle1+\angle2 = 180^{\circ}\) (consecutive - interior angles are supplementary).
Since \(\angle2 = 23^{\circ}\), then \(\angle1=180^{\circ}-\angle2\)
\(\angle1 = 157^{\circ}\)

Answer:

\(\angle1 = 157^{\circ}\), \(\angle2=23^{\circ}\)