PSLE Min has a triangular piece of paper LMN with ML = MN, ∠LMN = 84° and ∠NPP = 75°. LPN and MPN are straight lines. She folded it along the line PQ as shown.
- Find ∠r.
- Find ∠s.
(a)
Length of LM = Length of MN
Triangle LMN is an isosceles triangle.
∠MNL
= (180° - 84°) ÷ 2
= 96° ÷ 2
= 48° (Isosceles triangle)
∠r
= 180° - 75° - 48°
= 57° (Angles sum of triangle)
(b)
∠MLN = ∠MNL = 48°
∠t
= 180° - 75° - 75°
= 30° (Angles on a straight line)
∠s
= 180° - 48° - 30°
= 102° (Angles sum of triangle)
Answer(s): (a) 57°; (b) 102°