PSLE Usha has a triangular piece of paper QRS with RQ = RS, ∠QRS = 82° and ∠STT = 67°. QTS and RTS are straight lines. She folded it along the line TU as shown.
- Find ∠v.
- Find ∠w.
(a)
Length of QR = Length of RS
Triangle QRS is an isosceles triangle.
∠RSQ
= (180° - 82°) ÷ 2
= 98° ÷ 2
= 49° (Isosceles triangle)
∠v
= 180° - 67° - 49°
= 64° (Angles sum of triangle)
(b)
∠RQS = ∠RSQ = 49°
∠x
= 180° - 67° - 67°
= 46° (Angles on a straight line)
∠w
= 180° - 49° - 46°
= 85° (Angles sum of triangle)
Answer(s): (a) 64°; (b) 85°