PSLE Zoe has a triangular piece of paper KLM with LK = LM, ∠KLM = 76° and ∠MNN = 65°. 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° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠q
= 180° - 65° - 52°
= 63° (Angles sum of triangle)
(b)
∠LKM = ∠LMK = 52°
∠s
= 180° - 65° - 65°
= 50° (Angles on a straight line)
∠r
= 180° - 52° - 50°
= 78° (Angles sum of triangle)
Answer(s): (a) 63°; (b) 78°