PSLE Hazel has a triangular piece of paper NPQ with PN = PQ, ∠NPQ = 82° and ∠QRR = 68°. NRQ and PRQ are straight lines. She folded it along the line RS as shown.
- Find ∠t.
- Find ∠u.
(a)
Length of NP = Length of PQ
Triangle NPQ is an isosceles triangle.
∠PQN
= (180° - 82°) ÷ 2
= 98° ÷ 2
= 49° (Isosceles triangle)
∠t
= 180° - 68° - 49°
= 63° (Angles sum of triangle)
(b)
∠PNQ = ∠PQN = 49°
∠v
= 180° - 68° - 68°
= 44° (Angles on a straight line)
∠u
= 180° - 49° - 44°
= 87° (Angles sum of triangle)
Answer(s): (a) 63°; (b) 87°