Line ABC is a tangent to a circle at B. PQ Il AC and ∠QBC = 70°. ∠PBQ is =?

Correct option is C

Given:

∠QBC = 70°

PQ Il AC

Concept used:

The tangent-chord theorem (also known as alternate segment theorem ) states that in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

Solution:

∠QBC = ∠BQP  (PQ Il AC)

With the help of tangent cord  theorem

∠BPQ = ∠QBC

So, ∠BQP and ∠BPQ = 70°

So ∠PBQ = 180 - 140= 40°

∴ ∠PBQ is 40°