In the figure, DEF is parallel to GHJ and GF cuts ∠EGH equally. Given that ∠DEG = 46° and ∠EKF = 112°, find
- ∠i
- ∠j
(a)
∠DEG = ∠EGH (Alternate angles)
∠i
= 46° ÷ 2
= 23°
(b)
∠EGK = ∠i = 23°
∠j
= 112° - 23°
= 89° (Exterior angle of a triangle)
Answer(s): (a) 23°; (b) 89°