Q3 of 23 Page 1

Solve Question:

In the following figure, Q is the center of a circle and PM. PN are tangent segments to the circle, If ∠MPN = 60°, find ∠MQN.

The figure of the question is given below:


Given that ∠MPN = 60°


The above figure represents a quadrilateral PNQM


So, the sum of all angles of a quadrilateral is 360°


∴ ∠MQN + ∠QNP + ∠MPN + ∠PMQ = 360° .. eq(1)


Since PM is ⊥ MQ and PN is ⊥ QN


⇒ ∠QNP = ∠PMQ = 90°


By substituting all angles in eqn (1)


∠MQN + 90° + 60° + 90° = 360°


∴ ∠MQN = 120°


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