PSLE Victoria has a triangular piece of paper FGH with GF = GH, ∠FGH = 78° and ∠HJJ = 71°. FJH and GJH are straight lines. She folded it along the line JK as shown.
- Find ∠l.
- Find ∠m.
(a)
Length of FG = Length of GH
Triangle FGH is an isosceles triangle.
∠GHF
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠l
= 180° - 71° - 51°
= 58° (Angles sum of triangle)
(b)
∠GFH = ∠GHF = 51°
∠n
= 180° - 71° - 71°
= 38° (Angles on a straight line)
∠m
= 180° - 51° - 38°
= 91° (Angles sum of triangle)
Answer(s): (a) 58°; (b) 91°