In the figure, ∠UZD is a right-angled isosceles triangle. UD // WC , ∠BYX = 51°, ∠ZBA = 41° and ∠XAY = 54°. Find
- ∠UDZ
- ∠YWC
- ∠ACB
(a)
∠UDZ
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠ZBV = 45° (Corresponding angles, DU//BV)
∠YBW
= ∠ZBA + ∠ZBV
= 41° + 45°
= 86°
∠YWC
= 180° - ∠BYX - ∠YBW
= 180° - 51° - 86°
= 43° (Angles sum of triangle)
(c)
∠ABC
= 180° - ∠YBW
= 180° - 86°
= 94°(Angles in a straight line)
∠CAB = ∠YAZ = 54° (Vertically opposite angles)
∠ACB
= 180° - ∠CAB - ∠ABC
= 180° - 54° - 94°
= 32° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 43°; (c) 32°