DEFG is a square. KJF and EJG are straight lines. ED = EK and ∠JEK = 11°. Find
- ∠EDK
- ∠GFK
.
(a)
∠DEG = 45° (Right angle)
∠DEK
= ∠DEG - ∠JEK
= 45° - 11°
= 34°
∠EDK
= (180° - ∠DEK) ÷ 2
= (180° - 34°) ÷ 2
= 146° ÷ 2
= 73° (Isosceles triangle)
(b)
ED = EK = EF
KEF is an isosceles triangle.
∠EKF = ∠EFK (Isosceles triangle)
∠EFK
= (180° - ∠GEF - ∠JEK) ÷ 2
= (180° - 45° -11°) ÷ 2
= 124° ÷ 2
= 62°
∠GFK
= ∠EFG - ∠EFK
= 90° - 62°
= 28°
Answer(s): (a) 73°; (b) 28°
