In the figure, ∠PUY is a right-angled isosceles triangle. PY // RX , ∠WTS = 49°, ∠UWV = 40° and ∠SVT = 59°. Find
- ∠PYU
- ∠TRX
- ∠VXW
(a)
∠PYU
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠UWQ = 45° (Corresponding angles, YP//WQ)
∠TWR
= ∠UWV + ∠UWQ
= 40° + 45°
= 85°
∠TRX
= 180° - ∠WTS - ∠TWR
= 180° - 49° - 85°
= 46° (Angles sum of triangle)
(c)
∠VWX
= 180° - ∠TWR
= 180° - 85°
= 95°(Angles in a straight line)
∠XVW = ∠TVU = 59° (Vertically opposite angles)
∠VXW
= 180° - ∠XVW - ∠VWX
= 180° - 59° - 95°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 46°; (c) 26°
