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

[3 Marks]

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Solution

Given, AB is parallel to CD.

Therefore, $∠ E G C = 180^{\circ} - (2 x + 3 x)$ (Angles in linear pair) [1 Mark]

Also, $∠ E G C = ∠ A F G = 75^{\circ}$ (Corresponding angles) [1 Mark]

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

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

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

$\Rightarrow x = 21^{\circ}$ [1 Mark]

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