TRIGONNONETRY

ai)
∠AEB + ∠BAE + ∠ABE = 180°
∠AEB + ∠DAB/2 + ∠ABE = 180°
∠AEB + (128°/2)/2 + (180° - 128°)/2 = 180°
∠AEB + 32° + 26° = 180°
∠AEB = 122°
ii)
AE / sin∠ABE = AB / sin∠AEB ......(sine formula)
AE / sin26° = 20 / sin122°
AE = 10.33836 cm
iii)
△ABE
= (1/2) AB AE sin∠BAE
= (1/2) 20 * 10.33836 sin32°
= 54.78494 cm²

bi)
∠EAF = ∠CAE/2 = (∠BAE + ∠CAD)/2 = (32° + 128°/2)/2 = 48°
∠AEF = ∠AEC = 180° - ∠CAE - ∠ACD = 180° - 96° - (180° - 128°)/2
= 58°
∠AFE = 180° - 48° - 58° = 74°
AF / sin∠AEF = AE / sin∠AFE
AF / sin58° = 10.33836 / sin74°
AF = 9.12075 cm
ii)
△ACF = (1/2) AC AF sin∠EAF = (1/2) 20 * 9.12075 sin48°
= 67.780 cm²
iii)
△AEF = (1/2) AE AF sin∠EAF = (1/2) 10.33836 * 9.12075 sin48°
= 35.037 cm²