The figure is not drawn to scale. ∠GFH = 41°, GF = GH and FL//GK. Given that ∠r is
13 of ∠p and ∠r is 4 times of ∠q, find
- ∠r
- ∠n
(a)
r : p = 1 : 3
p = 3 r
q : r = 1 : 4
p = 3 x 4= 12
p : q : r = 12 : 1 : 4
∠GHF = 41° (Isosceles triangle)
∠FHJ
= 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°
∠r
= 4 x 1 u
= 4 x 13°
= 52°
(b)
∠GHF = ∠GFH = 41° (Isosceles triangle)
∠HMK = ∠HFL = 52° (Corresponding angles, FL//GK)
∠n
= 52° - 41°
= 11° (Exterior angle of a triangle)
Answer(s): (a) 52°; (b) 11°