In the figure, RSTU is a parallelogram. TW, WX and RS are straight lines. RUV is an isosceles triangle.
- Find ∠w.
- Find ∠x.
(a)
∠TWR = ∠SRX = 59° (Corresponding angles, RS//WT)
∠WVR
= 180° - ∠TWR - ∠WRV
= 180° - 59° - 18°
= 103° (Angles sum of triangle)
∠UVR
= 180° - 103°
= 77° (Angles on a straight line)
∠VUR = ∠UVR = 77° (Isosceles triangle)
∠w
= ∠VUR
= 77° (Corresponding angles, ST//RU)
(b)
∠x
= 180° - 77° - 77°
= 26° (Isosceles triangle RUV)
Answer(s): (a) 77°; (b) 26°