In the figure, NRUX is a rectangle, UVXY is a rhombus and RSTU is a parallelogram. ∠UVX = 76° and ∠TUV = 94°.
- Find ∠QUR
- Find ∠UTS
(a)
∠XYU = ∠XVU = 76°
∠YUX
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠QUR
= 90° - 52°
= 38°
(b)
∠RUT
= 360° - 94° - 90° - 52°
= 124° (Angles at a point)
∠STU
= 180° - 124°
= 56° (Interior Angles, RU//SF)
Answer(s): (a) 38°; (b) 56°