PSLE Risa has a triangular piece of paper PQR with QP = QR, ∠PQR = 78° and ∠RSS = 68°. 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° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠u
= 180° - 68° - 51°
= 61° (Angles sum of triangle)
(b)
∠QPR = ∠QRP = 51°
∠w
= 180° - 68° - 68°
= 44° (Angles on a straight line)
∠v
= 180° - 51° - 44°
= 85° (Angles sum of triangle)
Answer(s): (a) 61°; (b) 85°