Question

1. what are measures of ∠1 and ∠2?

Explanation:

Step1: Find the measure of ∠1

Since ∠1 and \(128^{\circ}\) form a linear pair, their sum is \(180^{\circ}\).
\(\angle1 = 180^{\circ}- 128^{\circ}\)
\(\angle1=52^{\circ}\)

Step2: Find the measure of ∠2

Use the triangle - angle sum theorem (the sum of interior angles of a triangle is \(180^{\circ}\)). Let the angles of the triangle be \(68^{\circ}\), \(\angle2\), and \(\angle1\).
We know \(\angle1 = 52^{\circ}\). Then \(68^{\circ}+\angle2+\angle1=180^{\circ}\)
Substitute \(\angle1 = 52^{\circ}\) into the equation: \(68^{\circ}+\angle2 + 52^{\circ}=180^{\circ}\)
\(\angle2=180^{\circ}-(68^{\circ}+ 52^{\circ})\)
\(\angle2=180^{\circ}-120^{\circ}\)
\(\angle2 = 60^{\circ}\)

Answer:

\(\angle1 = 52^{\circ}\) and \(\angle2=60^{\circ}\)