In the following figure, Q is the center of the circle. PM and PN are tangents to the circle. If ∠MPN = 40° , find ∠MQN.

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#### Solution

Given: ∠MPN = 40°

The line perpendicular to a radius of a circle at its outer end is a tangent to the circle.

∠PMQ = 90° and ∠QNP = 90°

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

∠MPN + ∠PMQ + ∠QNP + ∠MQN = 360°

40° + 90° + 90° + ∠MQN = 360°

220° + ∠MQN = 360°

∠MQN = 360° - 220°

∠MQN = 140°

Concept: Number of Tangents from a Point on a Circle

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