Question

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?

Answer 1

Explanation:

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

thus,

angle qsr = 58 degrees

Answer 2

• 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