The figure is not drawn to scale. ZAD is an equilateral triangle and CAB is an isosceles triangle. BAZ and ACE are straight lines and BZ//ED. ∠DAE = 90° and ∠CDA = 57°.
- Find ∠BAE.
- Find ∠ACB.
- Find ∠DCE.
(a)
∠DAZ = 60° (Equilateral triangle ZAY)
∠DAE = 90°
∠CDA = 57°
∠BAE
= 180° - ∠DAE - ∠DAZ
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠ACB
= (180° - ∠BAE ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠DCA
= 180° - ∠DAE - ∠CDA
= 180° - 90° - 57°
= 33°
∠DCE
= 180° - ∠DCA
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 147°
