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 consecutive - interior angles property

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary. So \(m\angle1 + 64^{\circ}=180^{\circ}\).

Step2: Solve for \(m\angle1\)

Subtract \(64^{\circ}\) from both sides of the equation \(m\angle1 + 64^{\circ}=180^{\circ}\). We get \(m\angle1+64^{\circ}-64^{\circ}=180^{\circ}-64^{\circ}\), so \(m\angle1 = 116^{\circ}\).

Step3: Use alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since \(\angle2\) and the \(64^{\circ}\) angle are alternate - interior angles, \(m\angle2 = 64^{\circ}\).

Answer:

\(m\angle1 = 116^{\circ}\), \(m\angle2 = 64^{\circ}\)