MQRU and MPSU are parallelograms and NTS is an isosceles triangle. Given that ∠NSP = 42°, ∠MUT = 64° and ∠QSR = 49°, find
- ∠PSQ,
- ∠QPS.
(a)
∠NST
= (180° - 23°) ÷ 2
= 78.5° (Isosceles triangle)
∠PSQ
= 180° - 78.5° - 42° - 49°
= 10.5° (Angles on a straight line)
(b)
∠QPS
= 180° - 49° -10.5°
= 120.5° (Interior angles)
Answer(s): (a) 10.5°; (b) 120.5°