The figure is not drawn to scale. ∠JHK = 41°, JH = JK and HN//JM. Given that ∠j is
13 of ∠h and ∠j is 4 times of ∠i, find
- ∠j
- ∠g
(a)
j : h = 1 : 3
h = 3 j
i : j = 1 : 4
h = 3 x 4= 12
h : i : j = 12 : 1 : 4
∠JKH = 41° (Isosceles triangle)
∠HKL
= 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°
∠j
= 4 x 1 u
= 4 x 13°
= 52°
(b)
∠JKH = ∠JHK = 41° (Isosceles triangle)
∠KPM = ∠KHN = 52° (Corresponding angles, HN//JM)
∠g
= 52° - 41°
= 11° (Exterior angle of a triangle)
Answer(s): (a) 52°; (b) 11°
