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°.
