In the figure, not drawn to scale, TVWX and SUXY are rhombuses. Given that ∠WVU = 115° and ∠TSY = 122°, find
- ∠SYU
- ∠UWT.
(a)
∠SYU
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, SY = SR)
(b)
∠UTX
= 180° - 115°
= 65° (Interior angles, WV//XQ)
∠YUS = ∠SYU = 29° (Isosceles Wriangle, SY = SR)
∠UWT
= 180° - 65° - 29°
= 86° (Angles sum of triangle, WUQ)
Answer(s): (a) 29°; (b) 86°