PSLE Gwen has a triangular piece of paper MNP with NM = NP, ∠MNP = 78° and ∠PQQ = 75°. 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° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠s
= 180° - 75° - 51°
= 54° (Angles sum of triangle)
(b)
∠NMP = ∠NPM = 51°
∠u
= 180° - 75° - 75°
= 30° (Angles on a straight line)
∠t
= 180° - 51° - 30°
= 99° (Angles sum of triangle)
Answer(s): (a) 54°; (b) 99°