In the figure, ∠XCG is a right-angled isosceles triangle. XG // ZF , ∠EBA = 52°, ∠CED = 43° and ∠ADB = 55°. Find
- ∠XGC
- ∠BZF
- ∠DFE
(a)
∠XGC
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠CEY = 45° (Corresponding angles, GX//EY)
∠BEZ
= ∠CED + ∠CEY
= 43° + 45°
= 88°
∠BZF
= 180° - ∠EBA - ∠BEZ
= 180° - 52° - 88°
= 40° (Angles sum of triangle)
(c)
∠DEF
= 180° - ∠BEZ
= 180° - 88°
= 92°(Angles in a straight line)
∠FDE = ∠BDC = 55° (Vertically opposite angles)
∠DFE
= 180° - ∠FDE - ∠DEF
= 180° - 55° - 92°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 40°; (c) 33°
