Question

select the correct answers. a pair of parallel lines is cut by a transversal. which group of angles measures 43°? a. angles 1, 2, 3 b. angles 2, 5, 4 c. angles 1, 3, 5 d. angles 5, 6, 7 e. angles 3, 4, 6

Explanation:

Step1: Find the measure of angle 1

The angle of \(137^{\circ}\) and angle 1 are supplementary (they form a linear - pair). So, \(\angle1=180^{\circ}-137^{\circ}=43^{\circ}\).

Step2: Find the measure of angle 3

Angle 1 and angle 3 are vertical angles. Since vertical angles are equal, \(\angle3 = \angle1=43^{\circ}\).

Step3: Find the measure of angle 5

The two lines are parallel and the transversal cuts them. Angle 1 and angle 5 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So, \(\angle5=\angle1 = 43^{\circ}\).

Answer:

C. angles 1, 3, 5