The figure is not drawn to scale. ∠XWY = 41°, XW = XY and WB//XA. Given that ∠x is
13 of ∠v and ∠x is 4 times of ∠w, find
- ∠x
- ∠t
(a)
x : v = 1 : 3
v = 3 x
w : x = 1 : 4
v = 3 x 4= 12
v : w : x = 12 : 1 : 4
∠XYW = 41° (Isosceles triangle)
∠WYZ
= 180° - 41°
= 139° (Angles on a straight line)
1 u + 4 u + 12 u + 139° = 360° (Sum of angles in a quadrilateral)
17 u = 360° - 139° = 221°
1 u = 221 ÷ 17 = 13°
∠x
= 4 x 1 u
= 4 x 13°
= 52°
(b)
∠XYW = ∠XWY = 41° (Isosceles triangle)
∠YCA = ∠YWB = 52° (Corresponding angles, WB//XA)
∠t
= 52° - 41°
= 11° (Exterior angle of a triangle)
Answer(s): (a) 52°; (b) 11°
