Question

I have doubt please help I'm solving this question....

Answer 1

Answer:

∠PRQ = 120 degrees

Step-by-step explanation:

Given, PQ is a chord of a circle and R is a point on the minor arc. If PT is a tangent at point P such that ∠QPT = 60 degrees then find ∠PRQ.

Let X be a point on the tangent PT.

Now, ∠QPT + ∠QPX = 180 degrees (Linear Pair)

∠QPX = 180 - ∠QPT = 180 - 60 = 120 degrees

NOtice that ∠QPX = ∠PRQ by Alternate Segment Theorem

Alternate Segment Theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

∠PRQ = 120 degrees.