In the figure, U is the centre of a semicircle and UQRS is a rhombus. Given that ∠UST = 30°, find
- ∠q
- ∠r
(a)
∠UST
= ∠UTS
= 30° (Isosceles triangle)
∠SUT
= 180° - 30° - 30°
= 120° (Angles sum of triangle)
∠q
= ∠SUT
= 120° (Corresponding angles)
(b)
∠r
= 180° - 120°
= 60° (Interior angles)
Answer(s): (a) 120°; (b) 60°