PSLE Opal has a triangular piece of paper PQR with QP = QR, ∠PQR = 76° and ∠RSS = 69°. 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° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠u
= 180° - 69° - 52°
= 59° (Angles sum of triangle)
(b)
∠QPR = ∠QRP = 52°
∠w
= 180° - 69° - 69°
= 42° (Angles on a straight line)
∠v
= 180° - 52° - 42°
= 86° (Angles sum of triangle)
Answer(s): (a) 59°; (b) 86°