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 = 49° and ∠XUY = 27°. Find
- ∠RUT
- ∠UWV
(a)
∠RUY
= (180° - 49°) ÷ 2
= 65.5° (Isosceles triangle)
∠RUT
= 180° - 65.5°
= 114.5° (Angles on a straight line)
(b)
∠WUV
= 65.5° - 27°
= 38.5°
∠UWV
= (180° - 38.5°) ÷ 2
= 70.75 ° (Isosceles triangle)
Answer(s): (a) 114.5°; (b) 70.75°