In the figure, ∠TYC is a right-angled isosceles triangle. TC // VB , ∠AXW = 52°, ∠YAZ = 38° and ∠WZX = 55°. Find
- ∠TCY
- ∠XVB
- ∠ZBA
(a)
∠TCY
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠YAU = 45° (Corresponding angles, CT//AU)
∠XAV
= ∠YAZ + ∠YAU
= 38° + 45°
= 83°
∠XVB
= 180° - ∠AXW - ∠XAV
= 180° - 52° - 83°
= 45° (Angles sum of triangle)
(c)
∠ZAB
= 180° - ∠XAV
= 180° - 83°
= 97°(Angles in a straight line)
∠BZA = ∠XZY = 55° (Vertically opposite angles)
∠ZBA
= 180° - ∠BZA - ∠ZAB
= 180° - 55° - 97°
= 28° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 45°; (c) 28°