In the figure, NRUX is a rectangle, UVXY is a rhombus and RSTU is a parallelogram. ∠UVX = 78° and ∠TUV = 91°.
- Find ∠QUR
- Find ∠UTS
(a)
∠XYU = ∠XVU = 78°
∠YUX
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠QUR
= 90° - 51°
= 39°
(b)
∠RUT
= 360° - 91° - 90° - 51°
= 128° (Angles at a point)
∠STU
= 180° - 128°
= 52° (Interior Angles, RU//SF)
Answer(s): (a) 39°; (b) 52°