In the figure, ∠WBF is a right-angled isosceles triangle. WF // YE , ∠DAZ = 48°, ∠BDC = 40° and ∠ZCA = 61°. Find
- ∠WFB
- ∠AYE
- ∠CED
(a)
∠WFB
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠BDX = 45° (Corresponding angles, FW//DX)
∠ADY
= ∠BDC + ∠BDX
= 40° + 45°
= 85°
∠AYE
= 180° - ∠DAZ - ∠ADY
= 180° - 48° - 85°
= 47° (Angles sum of triangle)
(c)
∠CDE
= 180° - ∠ADY
= 180° - 85°
= 95°(Angles in a straight line)
∠ECD = ∠ACB = 61° (Vertically opposite angles)
∠CED
= 180° - ∠ECD - ∠CDE
= 180° - 61° - 95°
= 24° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 47°; (c) 24°
