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Question

The given figure shows a pentagon ABCDE with sides AB and ED parallel to each other and $∠ B : ∠ C : ∠ D = 5 : 6 : 7.$ Write the value of $∠ A + ∠ E$ .

$∠ A + ∠ E = 180^{\circ}$
$∠ A + ∠ E = 90^{\circ}$
$∠ A + ∠ E = 145^{\circ}$
$∠ A + ∠ E = 160^{\circ}$

A

∠ A + ∠ E = 180^{\circ}

B

∠ A + ∠ E = 145^{\circ}

C

∠ A + ∠ E = 160^{\circ}

D

∠ A + ∠ E = 90^{\circ}

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Solution

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A pentagon ABCDE with sides AB and ED parallel to each other.
Then, AE behaves as a transversal.
$∠ B A E + ∠ A E D = 180^{o}$ (Sum of interior angles of the same side of transversal is supplementary)
So, $∠ A + ∠ E = 180^{o}$

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