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