PQRS is a quadrilateral and OPSR is a trapezium in which OP // SR and ∠QPS = 108°, ∠PSR = 122°, ∠QRS = 66° and SR = SP. Find
- ∠PQO
- ∠SPO
- ∠PRS.
(a)
∠PQO
= 360° - 122° -108° - 66°
= 64° (Sum of angles in a quadrilateral)
(b)
∠SPO
= 180° - 122°
= 58° (Interior angles, PO//SC)
(c)
∠PRS
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle)
Answer(s): (a) 64°; (b) 58°; (c) 29°