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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.
Solution
∠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°
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