Question

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

Answer 1

Seg PM and seg PN are tangents to the circle and seg QM and seg QN are the radii from the points of contacts.

m∠PMQ = m∠PNQ = 90°                  ... (Tangent is perpendicular to the radius) ... (1)

The sum of the measures of the angles of a quadrilateral is 360°.

m∠MPN + m∠PMQ + m∠MQN + m∠PNQ = 360°

60° + 90° + m∠MQN + 90° = 360°

240° + m∠MQN = 360°

m∠MQN = 360° – 240° = 120°                     ... [From (1)]