PSLE Penelope has a triangular piece of paper PQR with QP = QR, ∠PQR = 80° and ∠RSS = 72°. 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° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠u
= 180° - 72° - 50°
= 58° (Angles sum of triangle)
(b)
∠QPR = ∠QRP = 50°
∠w
= 180° - 72° - 72°
= 36° (Angles on a straight line)
∠v
= 180° - 50° - 36°
= 94° (Angles sum of triangle)
Answer(s): (a) 58°; (b) 94°