The figure is not drawn to scale. ∠PNQ = 41°, PN = PQ and NT//PS. Given that ∠q is
12 of ∠n and ∠q is 4 times of ∠p, find
- ∠q
- ∠m
(a)
q : n = 1 : 2
n = 2 q
p : q = 1 : 4
n = 2 x 4= 8
n : p : q = 8 : 1 : 4
∠PQN = 41° (Isosceles triangle)
∠NQR
= 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°
∠q
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠PQN = ∠PNQ = 41° (Isosceles triangle)
∠QUS = ∠QNT = 68° (Corresponding angles, NT//PS)
∠m
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°