In the figure, X is the centre of a semicircle and XTUV is a rhombus. Given that ∠XVW = 27°, find
- ∠q
- ∠r
(a)
∠XVW
= ∠XWV
= 27° (Isosceles triangle)
∠VXW
= 180° - 27° - 27°
= 126° (Angles sum of triangle)
∠q
= ∠VXW
= 126° (Corresponding angles)
(b)
∠r
= 180° - 126°
= 54° (Interior angles)
Answer(s): (a) 126°; (b) 54°