PSLE Xuan has a triangular piece of paper PQR with QP = QR, ∠PQR = 84° and ∠RSS = 66°. PSR and QSR are straight lines. She folded it along the line ST as shown.
- Find ∠u.
- Find ∠v.
(a)
Length of PQ = Length of QR
Triangle PQR is an isosceles triangle.
∠QRP
= (180° - 84°) ÷ 2
= 96° ÷ 2
= 48° (Isosceles triangle)
∠u
= 180° - 66° - 48°
= 66° (Angles sum of triangle)
(b)
∠QPR = ∠QRP = 48°
∠w
= 180° - 66° - 66°
= 48° (Angles on a straight line)
∠v
= 180° - 48° - 48°
= 84° (Angles sum of triangle)
Answer(s): (a) 66°; (b) 84°