The figure is not drawn to scale. ∠RQS = 41°, RQ = RS and QV//RU. Given that ∠i is
12 of ∠g and ∠i is 4 times of ∠h, find
- ∠i
- ∠f
(a)
i : g = 1 : 2
g = 2 i
h : i = 1 : 4
g = 2 x 4= 8
g : h : i = 8 : 1 : 4
∠RSQ = 41° (Isosceles triangle)
∠QST
= 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°
∠i
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠RSQ = ∠RQS = 41° (Isosceles triangle)
∠SWU = ∠SQV = 68° (Corresponding angles, QV//RU)
∠f
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
