Question

In quadrilateral PQRS, the exterior angle at Q measures 155 and PS = QR. What measure of ∠PSR would confirm that PQRS is a parallelogram?

Answer 1

The measure confirming that PQRS would be 25

Explanation:

It's easier if you draw it down.

1. We need to make this shape a parallelogram and the way we will do that is by making angle Q and angle S the same, because in parallelograms those opposite angles are required to be the same.

\

155 \

P \ -------------------------\ Q

\ 25 \

\ \ so that's your shape

S \______________\ R

2.We were given that the exterior angle of Q measures 155, and since exterior and interior angles combined make 180, then we can assume that the interior angle of Q is 25.

3. As mentioned before, in a parallelogram, opposite angles are the same and therefore PSR (which is just asking for the middle letter, S) is equal to 25 because Q is also 25.