The figure is not drawn to scale. ∠NMP = 41°, NM = NP and MS//NR. Given that ∠n is
13 of ∠k and ∠n is 4 times of ∠m, find
- ∠n
- ∠j
(a)
n : k = 1 : 3
k = 3 n
m : n = 1 : 4
k = 3 x 4= 12
k : m : n = 12 : 1 : 4
∠NPM = 41° (Isosceles triangle)
∠MPQ
= 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°
∠n
= 4 x 1 u
= 4 x 13°
= 52°
(b)
∠NPM = ∠NMP = 41° (Isosceles triangle)
∠PTR = ∠PMS = 52° (Corresponding angles, MS//NR)
∠j
= 52° - 41°
= 11° (Exterior angle of a triangle)
Answer(s): (a) 52°; (b) 11°
