In the figure, ∠AFK is a right-angled isosceles triangle. AK // CJ , ∠HED = 50°, ∠FHG = 43° and ∠DGE = 55°. Find
- ∠AKF
- ∠ECJ
- ∠GJH
(a)
∠AKF
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠FHB = 45° (Corresponding angles, KA//HB)
∠EHC
= ∠FHG + ∠FHB
= 43° + 45°
= 88°
∠ECJ
= 180° - ∠HED - ∠EHC
= 180° - 50° - 88°
= 42° (Angles sum of triangle)
(c)
∠GHJ
= 180° - ∠EHC
= 180° - 88°
= 92°(Angles in a straight line)
∠JGH = ∠EGF = 55° (Vertically opposite angles)
∠GJH
= 180° - ∠JGH - ∠GHJ
= 180° - 55° - 92°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 33°
