PQRS is a quadrilateral and OPSR is a trapezium in which OP // SR and ∠QPS = 109°, ∠PSR = 126°, ∠QRS = 64° and SR = SP. Find
- ∠PQO
- ∠SPO
- ∠PRS.
(a)
∠PQO
= 360° - 126° -109° - 64°
= 61° (Sum of angles in a quadrilateral)
(b)
∠SPO
= 180° - 126°
= 54° (Interior angles, PO//SC)
(c)
∠PRS
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle)
Answer(s): (a) 61°; (b) 54°; (c) 27°