In the figure, RSTU is a trapezium and RUVY is a rhombus. RU is parallel to ST and UV = UW. YUT and UXW are straight lines. ∠URY = 51° and ∠XUY = 27°. Find
- ∠RUT
- ∠UWV
(a)
∠RUY
= (180° - 51°) ÷ 2
= 64.5° (Isosceles triangle)
∠RUT
= 180° - 64.5°
= 115.5° (Angles on a straight line)
(b)
∠WUV
= 64.5° - 27°
= 37.5°
∠UWV
= (180° - 37.5°) ÷ 2
= 71.25 ° (Isosceles triangle)
Answer(s): (a) 115.5°; (b) 71.25°