PSLE Shiyun has a triangular piece of paper MNP with NM = NP, ∠MNP = 76° and ∠PQQ = 69°. MQP and NQP are straight lines. She folded it along the line QR as shown.
- Find ∠s.
- Find ∠t.
(a)
Length of MN = Length of NP
Triangle MNP is an isosceles triangle.
∠NPM
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠s
= 180° - 69° - 52°
= 59° (Angles sum of triangle)
(b)
∠NMP = ∠NPM = 52°
∠u
= 180° - 69° - 69°
= 42° (Angles on a straight line)
∠t
= 180° - 52° - 42°
= 86° (Angles sum of triangle)
Answer(s): (a) 59°; (b) 86°