If AB and CD are parallel, find the measure of angle x

15°

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105°

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21°

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51°

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Solution

The correct option is C
21°

AB is parallel to CD

Therefore,

$∠ E G C = 180^{\circ} - (2 x + 3 x)$

Also

$∠ E G C = ∠ A F G = 75^{\circ}$

$\Rightarrow 180^{\circ} - (2 x + 3 x) = 75^{\circ}$

$\Rightarrow - 5 x = 75^{\circ} - 180^{\circ}$

$\Rightarrow 5 x = 105^{\circ}$

$\Rightarrow x = 21^{\circ}$

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Similar questions

∠

In the given figure $C D ∥ E F$ and $A B$ is a transversal, and $∠ D G H = 2 x$ and $F H B = 5 x - 51$ degree.

Find the measure, in degrees, of $∠ B H E$

A B

B C

C D

∠ B A C = 15^{\circ}

A B C D

A B ∥ C D

∠ A : ∠ D = 2 : 3

∠ B : ∠ C = 7 : 8

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