In the figure, ∠ZEJ is a right-angled isosceles triangle. ZJ // BH , ∠GDC = 47°, ∠EGF = 42° and ∠CFD = 61°. Find
- ∠ZJE
- ∠DBH
- ∠FHG
(a)
∠ZJE
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠EGA = 45° (Corresponding angles, JZ//GA)
∠DGB
= ∠EGF + ∠EGA
= 42° + 45°
= 87°
∠DBH
= 180° - ∠GDC - ∠DGB
= 180° - 47° - 87°
= 46° (Angles sum of triangle)
(c)
∠FGH
= 180° - ∠DGB
= 180° - 87°
= 93°(Angles in a straight line)
∠HFG = ∠DFE = 61° (Vertically opposite angles)
∠FHG
= 180° - ∠HFG - ∠FGH
= 180° - 61° - 93°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 46°; (c) 26°
