Question

Find the ∠POQ if PQRS is a parallelogram and PO and OQ are angle bisectors.

$\left[3Marks\right]$

Answer 1

Since PQRS is a parallelogram, opposite sides angles are equal.
⇒ ∠P = ∠R = 80° and ∠Q = ∠S  ————– (i)
Now, ∠P + ∠Q + ∠R + ∠S = 360°  (Angle sum property of quadrilateral)
$\left[1Mark\right]$
⇒ 80° + 2∠Q + 80° = 360°  (from equation i)
⇒ ∠Q = 100°
Now, In ΔPOQ, ∠QPO = ½ ∠P = 40°
And ∠OQP = ½ ∠Q = 50°
$\left[1Mark\right]$
∠QPO + ∠OQP + ∠POQ = 180°  (Angle sum property of triangle)
⇒ 40° + 50° + ∠POQ = 180°
⇒ ∠POQ = 90°.
$\left[1Mark\right]$