Question

the figure shows two parallel lines intersected by two transversals. two of the angle measurements are given. find the measures of angles 1, 2, and 3.
the measure of angle 1 is (square^{circ}). (simplify your answer.)

Explanation:

Step1: Find the measure of angle 2

Since the sum of angles on a straight line is \(180^{\circ}\), and one of the angles is \(60^{\circ}\), then angle 2 is \(180 - 60- 63=57^{\circ}\) (using the property that the sum of angles around the intersection of transversals is \(180^{\circ}\)).

Step2: Find the measure of angle 1

Angle 1 and the \(63^{\circ}\) angle are vertical angles. Vertical angles are equal. So angle 1 is \(63^{\circ}\).

Answer:

\(63\)