In the given figure PQ || BC, $∠ 4 = ∠ 5$ and QB bisects $∠ P Q C$ . Find $∠ 1$ .

60

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Solution

The correct option is A 60
Given $∠ 4 = ∠ 5$ ,
and $∠ 2 = ∠ 5$
[PQB and QBC are alternate interior angles].
$∠ 2 = ∠ 3$
[Both are bisected so they are equal and half of PQC].
$∠ 4 = ∠ 5 = ∠ 3$ ,
Since all the angles are equal in the $Δ Q B C$ it is an equilateral triangle and hence each angle is $60^{\circ}$ .
$∠ 4 = ∠ 5 = ∠ 3 = 60^{\circ}$
$∠ 1 = ∠ 4 = 60^{\circ}$
[Corresponding angles].

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In the given figure PQ || BC, ∠4 = ∠5 and QB bisects ∠PQC. Find ∠1. 60

In the given figure PQ || BC, $∠ 4 = ∠ 5$ and QB bisects $∠ P Q C$ . Find $∠ 1$ .

60