PSLE Penelope has a triangular piece of paper JKL with KJ = KL, ∠JKL = 82° and ∠LMM = 67°. JML and KML are straight lines. She folded it along the line MN as shown.
- Find ∠p.
- Find ∠q.
(a)
Length of JK = Length of KL
Triangle JKL is an isosceles triangle.
∠KLJ
= (180° - 82°) ÷ 2
= 98° ÷ 2
= 49° (Isosceles triangle)
∠p
= 180° - 67° - 49°
= 64° (Angles sum of triangle)
(b)
∠KJL = ∠KLJ = 49°
∠r
= 180° - 67° - 67°
= 46° (Angles on a straight line)
∠q
= 180° - 49° - 46°
= 85° (Angles sum of triangle)
Answer(s): (a) 64°; (b) 85°