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