The figure is not drawn to scale. ∠NMP = 41°, NM = NP and MS//NR. Given that ∠e is
12 of ∠c and ∠e is 4 times of ∠d, find
- ∠e
- ∠b
(a)
e : c = 1 : 2
c = 2 e
d : e = 1 : 4
c = 2 x 4= 8
c : d : e = 8 : 1 : 4
∠NPM = 41° (Isosceles triangle)
∠MPQ
= 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°
∠e
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠NPM = ∠NMP = 41° (Isosceles triangle)
∠PTR = ∠PMS = 68° (Corresponding angles, MS//NR)
∠b
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
