139k views
23 votes
Quadrilateral PQRS, shown below, is a parallelogram. QS is a diagonal. PQ ║ SR and PS ║ QR.

The measure of ∠PQS is 58° degrees. What is the measure in degrees of ∠QSR?

Quadrilateral PQRS, shown below, is a parallelogram. QS is a diagonal. PQ ║ SR and-example-1
User Ahmadreza
by
7.3k points

2 Answers

12 votes

Explanation:

angle pqs = angle qsr (alternate interior angles are equal in a parallelogram).

thus,

angle qsr = 58 degrees

User Joris Kluivers
by
7.6k points
12 votes

Answer:

  • 58°


\:

Explanation:

  • As, Quadrilateral PQRS is a parallelogram and PQ ║ SR and PS ║ QR where QS is the transversal

And, it is given that the measure of ∠PQS is 58°.

So,


\bf \qquad∠QSR = ∠PQS \\ \\


\bf \qquad \implies∠QSR = 58° \: \: [Alternate \: interior \: angles] \\ \\

Let's know something about Alternate interior angles :

  • If a transversal intersects two parallel lines, then each pair of alternate interior angle is equal
User Corrin
by
7.1k points