PQ||SR and PS||QR
a = ?

a = 80°

Solution:

Given data:

PQ || SR and PS || QR

This implies that PQRS is a parallelogram.

PR is a transversal for the parallel lines PQ and SR.

∠SPR and ∠PRQ are alternate interior angles.

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

∠SPR ≅ ∠PRQ

m∠SPR = m∠PRQ

m∠SPR =  80°

⇒ a = 80°

Hence the measure of a is 80°.