The given figure shows an isosceles triangle PQR in which PQ = PR. L and M are the mid-points of sides PQ and PR respectively.

If ∠MLQ = 110°, then what is the measure of ∠PRQ?

It is given that, L and M are the mid-points of sides PQ and PR respectively.

We know that the line segment joining the mid-points of any two sides of a triangle is parallel to the third side.

∴ LM || QR

LM || QR and PQ is the transversal.

∴ ∠MLQ + ∠LQR = 180°        [Interior angles on the same side of the transversal are supplementary]

⇒ ∠LQR = 180° − ∠MLQ

⇒ ∠LQR = 180 − 110° = 70°

∴ ∠PQR = 70°

ΔPQR is an isosceles triangle in which PQ = PR.

∴ ∠PQR = ∠PRQ       (Equal sides have equal angles opposite to them)

⇒ ∠PRQ = 70°

Thus, the measure of ∠PRQ is 70°.