PSLE Xylia has a triangular piece of paper DEF with ED = EF, ∠DEF = 78° and ∠FGG = 70°. DGF and EGF are straight lines. She folded it along the line GH as shown.
- Find ∠j.
- Find ∠k.
(a)
Length of DE = Length of EF
Triangle DEF is an isosceles triangle.
∠EFD
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠j
= 180° - 70° - 51°
= 59° (Angles sum of triangle)
(b)
∠EDF = ∠EFD = 51°
∠l
= 180° - 70° - 70°
= 40° (Angles on a straight line)
∠k
= 180° - 51° - 40°
= 89° (Angles sum of triangle)
Answer(s): (a) 59°; (b) 89°