In the figure, Q is the centre of the circle, MQ is parallel to NP and ∠NQP = 112°. Find the values of
- ∠g
- ∠h
- ∠i
(a)
∠g
= (180° - 112°) ÷ 2
= 34° (Angle properties within a circle)
(b)
∠MQN = ∠g = 34° (Alternate angles)
∠h
= (180° - 34°) ÷ 2
= 73° (Angle properties within a circle)
(c)
∠i
= 360° - 112° - 34°
= 214° (Angles at a point)
Answer(s): (a) 34°; (b) 73°; (c) 214°