In the figure, ∠SXB is a right-angled isosceles triangle. SB // UA , ∠ZWV = 50°, ∠XZY = 41° and ∠VYW = 53°. Find
- ∠SBX
- ∠WUA
- ∠YAZ
(a)
∠SBX
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠XZT = 45° (Corresponding angles, BS//ZT)
∠WZU
= ∠XZY + ∠XZT
= 41° + 45°
= 86°
∠WUA
= 180° - ∠ZWV - ∠WZU
= 180° - 50° - 86°
= 44° (Angles sum of triangle)
(c)
∠YZA
= 180° - ∠WZU
= 180° - 86°
= 94°(Angles in a straight line)
∠AYZ = ∠WYX = 53° (Vertically opposite angles)
∠YAZ
= 180° - ∠AYZ - ∠YZA
= 180° - 53° - 94°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 44°; (c) 33°