Question

In Exercises 32 and 33, use the diagram.

Which numbered angles have the same measure as $\angle 1$? Explain your reasoning.

Short answer

$m\angle 1=m\angle 3=m\angle 4=m\angle 7$

Step-by-step solution

Step 1. Given Information.

The figure is shown below.

Step 2. Concept Used.

In the parallel line and its transversal corresponding angles are equal, vertically opposite angles are equal and also alternate exterior angles are equal.

Step 3. Explanation.

In the diagram,

$m\angle 1=m\angle 3$ (Vertically opposite angles)

$m\angle 1=m\angle 4$ (Corresponding angles)

$m\angle 1=m\angle 7$ (Alternate exterior angles)

Thus, $m\angle 1=m\angle 3=m\angle 4=m\angle 7$.