The figure is not drawn to scale. ∠UTV = 41°, UT = UV and TY//UX. Given that ∠n is
12 of ∠k and ∠n is 4 times of ∠m, find
- ∠n
- ∠j
(a)
n : k = 1 : 2
k = 2 n
m : n = 1 : 4
k = 2 x 4= 8
k : m : n = 8 : 1 : 4
∠UVT = 41° (Isosceles triangle)
∠TVW
= 180° - 41°
= 139° (Angles on a straight line)
1 u + 4 u + 8 u + 139° = 360° (Sum of angles in a quadrilateral)
13 u = 360° - 139° = 221°
1 u = 221 ÷ 13 = 17°
∠n
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠UVT = ∠UTV = 41° (Isosceles triangle)
∠VZX = ∠VTY = 68° (Corresponding angles, TY//UX)
∠j
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
