Question

In the adjoining figure circle with Centre, Q touches the sides of ∠MPN at M and N. If ∠MPN = 40°, find measure of ∠MQN.

Answer 1

∠MPN = 40°      ....[Given]

`{:(∠"QMP" = 90^circ),(∠"QNP" = 90^circ):}}` .....[Tangent theorem]

In ▢MQNP,

∠MPN + ∠QMP + ∠QNP + ∠MQN = 360°    ...[Sum of the measures of the angles of a quadrilateral is 360°]

∴ 40° + 90° + 90° + ∠MQN = 360°

∴ 220° + ∠MQN = 360°

∴ ∠MQN = 360° − 220°

∴ ∠MQN = 140°