Which Theorem Should We Apply?

Let us join the point $P$ to point $Q$ to form a straight line $PQ$ .

By alternate segment theorem , in the triangle $PQR$ , we have

$\angle PQR=50, \angle QPR=60 .$

Because the sum of angles of a triangle is $180^\circ$ , then $\angle PRQ=180^\circ-50^\circ-60^\circ = \boxed{70^\circ }$ .

Triangle POR is isosceles with equal angles of 40º (90-50)

Triangle QOR is isosceles with equal angles of 30º (90-60)

That mean angle <PRQ= 40 +30 = 70º

let angel prq=x .angel between 2tangent=y angel opy.oqr=90 angel poq=2x 2x=180-y ,x=360-50-60-y then x=70

If an angle is formed between a chord and a tangent. That angle is half the arc measure that is intercepted by the chord. This theorem is a hint to the solution!