Question

1. find the measures of the numbered angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle 1 and the 67° angle are vertical angles, so $\angle1 = 67^{\circ}$.

Step2: Use linear - pair property

Angle 1 and angle 2 form a linear pair (sum to 180°). So $\angle2=180^{\circ}-\angle1 = 180 - 67=113^{\circ}$.

Step3: Use vertical - angle property again

Angle 2 and angle 3 are vertical angles. So $\angle3=\angle2 = 113^{\circ}$.

Answer:

$\angle1 = 67^{\circ}$, $\angle2 = 113^{\circ}$, $\angle3 = 113^{\circ}$