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 = 160^{\circ}

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∠ A + ∠ E = 180^{\circ}

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∠ A + ∠ E = 90^{\circ}

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∠ A + ∠ E = 145^{\circ}

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Solution

The correct option is A $∠ A + ∠ E = 180^{\circ}$
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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Similar questions

The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and $∠ B : ∠ C | ∠ D = 5 : 6 : 7$ .

(i) Using formula, find the sum of interior angles of the pentagon.

(ii) Write the value of $∠ A + ∠ E$

(iii) Find angles B, C and D.

∠ A : ∠ E : ∠ D = 3 : 4 : 5.

A B C D E, A B

D C

∠ A : ∠ E, ∠ D = 3 : 4 : 5

∠ E

∠ A : ∠ E : ∠ D = 3 : 4 : 5

∠ E

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