In the figure, not drawn to scale, STUV is a square, UVW is an equilateral triangle, UWXY is a rhombus, and TU = WU. Find
- ∠WXY
- ∠SWT
(a)
∠VUW = 60°
∠TUW
= 90° - 60°
= 30°
UW = UT
∠UWT
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠WXY
= 180° - 75°
= 105° (Interior angles)
(b)
∠UTW = ∠UWT = 75°
∠STW
= 90° - 75°
= 15°
∠SWT
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°