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प्रश्न
In the adjoining figure circle with Centre, Q touches the sides of ∠MPN at M and N. If ∠MPN = 40°, find measure of ∠MQN.
बेरीज
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उत्तर
∠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°
shaalaa.com
Tangent Segment Theorem
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