PQRS is a quadrilateral and OPSR is a trapezium in which OP // SR and ∠QPS = 108°, ∠PSR = 128°, ∠QRS = 65° and SR = SP. Find
- ∠PQO
- ∠SPO
- ∠PRS.
(a)
∠PQO
= 360° - 128° -108° - 65°
= 59° (Sum of angles in a quadrilateral)
(b)
∠SPO
= 180° - 128°
= 52° (Interior angles, PO//SC)
(c)
∠PRS
= (180° - 128°) ÷ 2
= 52 ÷ 2
= 26° (Isosceles triangle)
Answer(s): (a) 59°; (b) 52°; (c) 26°