PSLE Dana has a triangular piece of paper MNP with NM = NP, ∠MNP = 80° and ∠PQQ = 65°. 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° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠s
= 180° - 65° - 50°
= 65° (Angles sum of triangle)
(b)
∠NMP = ∠NPM = 50°
∠u
= 180° - 65° - 65°
= 50° (Angles on a straight line)
∠t
= 180° - 50° - 50°
= 80° (Angles sum of triangle)
Answer(s): (a) 65°; (b) 80°