PSLE Min has a triangular piece of paper PQR with QP = QR, ∠PQR = 82° and ∠RSS = 75°. 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° - 82°) ÷ 2
= 98° ÷ 2
= 49° (Isosceles triangle)
∠u
= 180° - 75° - 49°
= 56° (Angles sum of triangle)
(b)
∠QPR = ∠QRP = 49°
∠w
= 180° - 75° - 75°
= 30° (Angles on a straight line)
∠v
= 180° - 49° - 30°
= 101° (Angles sum of triangle)
Answer(s): (a) 56°; (b) 101°