In the figure, RSTU is a parallelogram. TW, WX and RS are straight lines. RUV is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠TWR = ∠SRX = 58° (Corresponding angles, RS//WT)
∠WVR
= 180° - ∠TWR - ∠WRV
= 180° - 58° - 21°
= 101° (Angles sum of triangle)
∠UVR
= 180° - 101°
= 79° (Angles on a straight line)
∠VUR = ∠UVR = 79° (Isosceles triangle)
∠q
= ∠VUR
= 79° (Corresponding angles, ST//RU)
(b)
∠r
= 180° - 79° - 79°
= 22° (Isosceles triangle RUV)
Answer(s): (a) 79°; (b) 22°