In the figure, Q is the centre of the circle, MQ is parallel to NP and ∠NQP = 104°. Find the values of
- ∠i
- ∠j
- ∠k
(a)
∠i
= (180° - 104°) ÷ 2
= 38° (Angle properties within a circle)
(b)
∠MQN = ∠i = 38° (Alternate angles)
∠j
= (180° - 38°) ÷ 2
= 71° (Angle properties within a circle)
(c)
∠k
= 360° - 104° - 38°
= 218° (Angles at a point)
Answer(s): (a) 38°; (b) 71°; (c) 218°