In the figure, ∠VAE is a right-angled isosceles triangle. VE // XD , ∠CZY = 52°, ∠ACB = 41° and ∠YBZ = 55°. Find
- ∠VEA
- ∠ZXD
- ∠BDC
(a)
∠VEA
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠ACW = 45° (Corresponding angles, EV//CW)
∠ZCX
= ∠ACB + ∠ACW
= 41° + 45°
= 86°
∠ZXD
= 180° - ∠CZY - ∠ZCX
= 180° - 52° - 86°
= 42° (Angles sum of triangle)
(c)
∠BCD
= 180° - ∠ZCX
= 180° - 86°
= 94°(Angles in a straight line)
∠DBC = ∠ZBA = 55° (Vertically opposite angles)
∠BDC
= 180° - ∠DBC - ∠BCD
= 180° - 55° - 94°
= 31° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 31°
