In the figure, not drawn to scale, TUVW is a square, VWX is an equilateral triangle, VXYZ is a rhombus, and UV = XV. Find
- ∠XYZ
- ∠TXU
(a)
∠WVX = 60°
∠UVX
= 90° - 60°
= 30°
VX = VU
∠VXU
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠XYZ
= 180° - 75°
= 105° (Interior angles)
(b)
∠VUX = ∠VXU = 75°
∠TUX
= 90° - 75°
= 15°
∠TXU
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°