PSLE Victoria has a triangular piece of paper LMN with ML = MN, ∠LMN = 82° and ∠NPP = 74°. 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° - 82°) ÷ 2
= 98° ÷ 2
= 49° (Isosceles triangle)
∠r
= 180° - 74° - 49°
= 57° (Angles sum of triangle)
(b)
∠MLN = ∠MNL = 49°
∠t
= 180° - 74° - 74°
= 32° (Angles on a straight line)
∠s
= 180° - 49° - 32°
= 99° (Angles sum of triangle)
Answer(s): (a) 57°; (b) 99°