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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.
Solution
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)]
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