In the figure, ∠AFK is a right-angled isosceles triangle. AK // CJ , ∠HED = 49°, ∠FHG = 37° and ∠DGE = 61°. Find
- ∠AKF
- ∠ECJ
- ∠GJH
(a)
∠AKF
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠FHB = 45° (Corresponding angles, KA//HB)
∠EHC
= ∠FHG + ∠FHB
= 37° + 45°
= 82°
∠ECJ
= 180° - ∠HED - ∠EHC
= 180° - 49° - 82°
= 49° (Angles sum of triangle)
(c)
∠GHJ
= 180° - ∠EHC
= 180° - 82°
= 98°(Angles in a straight line)
∠JGH = ∠EGF = 61° (Vertically opposite angles)
∠GJH
= 180° - ∠JGH - ∠GHJ
= 180° - 61° - 98°
= 21° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 49°; (c) 21°