PSLE Gwen has a triangular piece of paper DEF with ED = EF, ∠DEF = 76° and ∠FGG = 71°. 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° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠j
= 180° - 71° - 52°
= 57° (Angles sum of triangle)
(b)
∠EDF = ∠EFD = 52°
∠l
= 180° - 71° - 71°
= 38° (Angles on a straight line)
∠k
= 180° - 52° - 38°
= 90° (Angles sum of triangle)
Answer(s): (a) 57°; (b) 90°