In the figure, ∠CHM is a right-angled isosceles triangle. CM // EL , ∠KGF = 51°, ∠HKJ = 42° and ∠FJG = 54°. Find
- ∠CMH
- ∠GEL
- ∠JLK
(a)
∠CMH
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠HKD = 45° (Corresponding angles, MC//KD)
∠GKE
= ∠HKJ + ∠HKD
= 42° + 45°
= 87°
∠GEL
= 180° - ∠KGF - ∠GKE
= 180° - 51° - 87°
= 42° (Angles sum of triangle)
(c)
∠JKL
= 180° - ∠GKE
= 180° - 87°
= 93°(Angles in a straight line)
∠LJK = ∠GJH = 54° (Vertically opposite angles)
∠JLK
= 180° - ∠LJK - ∠JKL
= 180° - 54° - 93°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 33°
