In the figure, not drawn to scale. EFGH is a square. GHJ is an equilateral triangle and EG is a straight line. Find
- Three-fifths of ∠EKJ
- Four times of ∠JGK
(a)
∠HEG = 45° (Right angle)
∠KHG = 60° (Equilateral triangle)
∠EHK
= 90° - ∠KHG
= 90° - 60°
= 30°
∠EKJ
= 30° + 45° (Exterior angle of a triangle)
= 75°
Three-fifths of ∠EKJ
=
35 x 75°
= 45°
(b)
∠JKG
= 180° - ∠EKJ
= 180° - 75°
= 105° (Angles on a straight line)
∠JGK
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Four times of ∠JGK
= 4 x 15°
= 60°
Answer(s): (a) 45°; (b) 60°
