In the figure, NRUX is a rectangle, UVXY is a rhombus and RSTU is a parallelogram. ∠UVX = 80° and ∠TUV = 96°.
- Find ∠QUR
- Find ∠UTS
(a)
∠XYU = ∠XVU = 80°
∠YUX
= (180° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠QUR
= 90° - 50°
= 40°
(b)
∠RUT
= 360° - 96° - 90° - 50°
= 124° (Angles at a point)
∠STU
= 180° - 124°
= 56° (Interior Angles, RU//SF)
Answer(s): (a) 40°; (b) 56°