PSLE Xuan has a triangular piece of paper KLM with LK = LM, ∠KLM = 78° and ∠MNN = 71°. KNM and LNM are straight lines. She folded it along the line NP as shown.
- Find ∠q.
- Find ∠r.
(a)
Length of KL = Length of LM
Triangle KLM is an isosceles triangle.
∠LMK
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠q
= 180° - 71° - 51°
= 58° (Angles sum of triangle)
(b)
∠LKM = ∠LMK = 51°
∠s
= 180° - 71° - 71°
= 38° (Angles on a straight line)
∠r
= 180° - 51° - 38°
= 91° (Angles sum of triangle)
Answer(s): (a) 58°; (b) 91°