Question

two streets are parallel as they pass through columbus avenue. find the measures of ∠1 and ∠2. justify your steps. ∠1 and the angle labeled 64° are consecutive interior angles. m∠1 + 64° =
□ ° m∠1 + 64° - 64° =
□ ° - 64° m∠1 =
□ ° ∠2 and the angle labeled 64° are alternate interior angles. m∠2 =
□ °

Explanation:

Step1: Use alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since ∠2 and the 64° angle are alternate - interior angles, m∠2 = 64°.

Step2: Use consecutive - interior angles property

Consecutive - interior angles are supplementary when two parallel lines are cut by a transversal. Let m∠1=x. We know that x + 64°=180°. Solving for x: x=180° - 64°=116°. So m∠1 = 116°.

Answer:

m∠1 = 116°, m∠2 = 64°