In the figure, ∠SXB is a right-angled isosceles triangle. SB // UA , ∠ZWV = 48°, ∠XZY = 39° and ∠VYW = 54°. Find
- ∠SBX
- ∠WUA
- ∠YAZ
(a)
∠SBX
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠XZT = 45° (Corresponding angles, BS//ZT)
∠WZU
= ∠XZY + ∠XZT
= 39° + 45°
= 84°
∠WUA
= 180° - ∠ZWV - ∠WZU
= 180° - 48° - 84°
= 48° (Angles sum of triangle)
(c)
∠YZA
= 180° - ∠WZU
= 180° - 84°
= 96°(Angles in a straight line)
∠AYZ = ∠WYX = 54° (Vertically opposite angles)
∠YAZ
= 180° - ∠AYZ - ∠YZA
= 180° - 54° - 96°
= 30° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 48°; (c) 30°
