Question

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$\huge\sf\pink{Question}$

In the given figure, AB || CD and XY is a transversal line intersects AB and CD at E and G respectively. If EF and GF are the bisectors of ∠BEG and ∠DGE respectively, then the measure of ∠EFG is equal to___?

$\sf\bold{Explanation\: required}$

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Answer 1

I think it's answer should be

Option 4.) 90°

because angle EFG in figure is right angle.

Answer 2

Answer: (4) 90°.

Explanation:

We know, co-interior angles are supplementary to each other.

∴ ∠BEG + ∠EGD = 180°

=> ∠FEG + ∠FGE = 90° __(A)

Now, by angle sum property of triangle,

Sum of all angles of ∆ = 180°

=> ∠EFG = 180° - (∠FEG + ∠FGE)

=> ∠EFG = 180° - 90° = 90°.

Tip: When a transversal line passes through two // lines, then the quad. formed by joining the interior angle bisectors of co-interior angles make a rectangle.