In the figure, ∠QVZ is a right-angled isosceles triangle. QZ // SY , ∠XUT = 52°, ∠VXW = 39° and ∠TWU = 60°. Find
- ∠QZV
- ∠USY
- ∠WYX
(a)
∠QZV
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠VXR = 45° (Corresponding angles, ZQ//XR)
∠UXS
= ∠VXW + ∠VXR
= 39° + 45°
= 84°
∠USY
= 180° - ∠XUT - ∠UXS
= 180° - 52° - 84°
= 44° (Angles sum of triangle)
(c)
∠WXY
= 180° - ∠UXS
= 180° - 84°
= 96°(Angles in a straight line)
∠YWX = ∠UWV = 60° (Vertically opposite angles)
∠WYX
= 180° - ∠YWX - ∠WXY
= 180° - 60° - 96°
= 24° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 44°; (c) 24°
