If triangles ABC and PQR are both isosceles with AB=AC and PQ=PR, respectively. If also AB=PQ and BC=QR and angle B=50°, then what is the measure of angle R?

50°

We are given that :-  AB = AC , PQ = PR  & AB = PQ , BC = QR

In triangle ABC and triangle PQR

AB = PQ

BC = QR

AC = PR

So, by using ( side - side - side ) congruency equation.

△ ABC ≅ △ PQR 

So, ∠ABC = ∠PQR

⇒ ∠PQR  = 50º

$$And\; we\; are\; given\; that\; PQ\; =PR$$

$$\{\; In\; a\; triangle\; ,\; angle\; made\; by\; same\; sides\; are\; same\; \}$$

∠PQR = ∠PRQ

⇒ ∠PRQ = 50º