Question

m∠1 = 114°
m∠2 = 114°
tell which postulates or theorems you used.
postulates
theorem
corresponding angles theorem

Explanation:

Step1: Identify angle - relationship

The angle adjacent to the $66^{\circ}$ angle and $\angle1$ are corresponding angles. Also, the angle adjacent to the $66^{\circ}$ angle and $\angle2$ are corresponding angles.

Step2: Calculate the adjacent - angle to $66^{\circ}$

Since a straight - line has an angle measure of $180^{\circ}$, if one angle is $66^{\circ}$, the adjacent angle to it is $180 - 66=114^{\circ}$.

Step3: Apply the corresponding - angles theorem

Corresponding angles formed by two parallel lines and a transversal are congruent. So, $m\angle1 = 114^{\circ}$ and $m\angle2 = 114^{\circ}$ because they are corresponding to the $114^{\circ}$ angle adjacent to the $66^{\circ}$ angle.

Answer:

Postulates: None
Theorem: Corresponding Angles Theorem