In the figure, ∠TYC is a right-angled isosceles triangle. TC // VB , ∠AXW = 48°, ∠YAZ = 41° and ∠WZX = 58°. Find
- ∠TCY
- ∠XVB
- ∠ZBA
(a)
∠TCY
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠YAU = 45° (Corresponding angles, CT//AU)
∠XAV
= ∠YAZ + ∠YAU
= 41° + 45°
= 86°
∠XVB
= 180° - ∠AXW - ∠XAV
= 180° - 48° - 86°
= 46° (Angles sum of triangle)
(c)
∠ZAB
= 180° - ∠XAV
= 180° - 86°
= 94°(Angles in a straight line)
∠BZA = ∠XZY = 58° (Vertically opposite angles)
∠ZBA
= 180° - ∠BZA - ∠ZAB
= 180° - 58° - 94°
= 28° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 46°; (c) 28°
