In the figure, NRUX is a rectangle, UVXY is a rhombus and RSTU is a parallelogram. ∠UVX = 72° and ∠TUV = 97°.
- Find ∠QUR
- Find ∠UTS
(a)
∠XYU = ∠XVU = 72°
∠YUX
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠QUR
= 90° - 54°
= 36°
(b)
∠RUT
= 360° - 97° - 90° - 54°
= 119° (Angles at a point)
∠STU
= 180° - 119°
= 61° (Interior Angles, RU//SF)
Answer(s): (a) 36°; (b) 61°