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