In the figure, ∠UZD is a right-angled isosceles triangle. UD // WC , ∠BYX = 49°, ∠ZBA = 42° and ∠XAY = 61°. Find
- ∠UDZ
- ∠YWC
- ∠ACB
(a)
∠UDZ
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠ZBV = 45° (Corresponding angles, DU//BV)
∠YBW
= ∠ZBA + ∠ZBV
= 42° + 45°
= 87°
∠YWC
= 180° - ∠BYX - ∠YBW
= 180° - 49° - 87°
= 44° (Angles sum of triangle)
(c)
∠ABC
= 180° - ∠YBW
= 180° - 87°
= 93°(Angles in a straight line)
∠CAB = ∠YAZ = 61° (Vertically opposite angles)
∠ACB
= 180° - ∠CAB - ∠ABC
= 180° - 61° - 93°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 44°; (c) 26°
