In the figure, not drawn to scale, RSTU is a square, TUV is an equilateral triangle, TVWX is a rhombus, and ST = VT. Find
- ∠VWX
- ∠RVS
(a)
∠UTV = 60°
∠STV
= 90° - 60°
= 30°
TV = TS
∠TVS
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠VWX
= 180° - 75°
= 105° (Interior angles)
(b)
∠TSV = ∠TVS = 75°
∠RSV
= 90° - 75°
= 15°
∠RVS
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°