Question

In the given figure PQ || BC, $\angle 4=\angle 5$ and QB bisects $\angle PQC$. Find $\angle 1$.
[3 Marks]

Answer 1

Given, $\angle 4=\angle 5$,
$\angle 2=\angle 5$ ..........(1)
[Alternate interior angles]. [1 Mark]

$\angle 2=\angle 3$ ............(2)
[Both are bisected so they are equal and half of PQC].
From (1) and (2),
$\angle 4=\angle 5=\angle 3$,
Since all the angles are equal in the $\Delta QBC$ it is an equilateral triangle and hence each angle is ${60}^{\circ }$.
[1 Mark]

$\angle 4=\angle 5=\angle 3={60}^{\circ }$

$\angle 1=\angle 4={60}^{\circ }$ [Corresponding angles]. [ 1 Mark]