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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___?

$\sf\bold{Explanation\: required}$​

Answer 1

Answer:

90

Step-by-step explanation:

As BEG and DGE are int. angles and there sum is 180.

so

if we take common 0.5 we get 90

so

FEG + EGF = 90

therefore

the other angle have to be 90

to follow angle sum property

Answer 2

Answer:

Option (4)

Step-by-step explanation:

Given :-

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

To find :-

Find the measure of ∠EFG ?

Solution :-

Given that

AB || CD and XY is a transversal line intersects AB and CD at E and G respectively.

We know that

If two parallel lines Intersected by a transversal then The interior angles on the same side to the transversal are supplementary.

=>∠BEG+ ∠DGE = 180° ------(1)

Given that

EF and GF are the bisectors of ∠BEG and ∠DGE respectively.

=> ∠BEG = ∠BEF + ∠FEG -----(2)

∠BEF = ∠FEG

and

∠DGE = ∠DGF + ∠FGE ---------(3)

∠DGF = ∠FGE

equation (1) becomes

=> ∠BEF + ∠FEG + ∠DGF + ∠FGE = 180°

=> ∠FEG + ∠FEG+ ∠FGE+∠FGE = 180°

=>2 ∠FEG +2∠FGE= 180°

=> 2(∠FEG +∠FGE ) = 180°

=> ∠FEG +∠FGE= 180°/2

=> ∠FEG +∠FGE = 90° ------(4)

We know that

The sum of all the three angles in a triangle is 180°

In ∆ EFG,

∠FEG +∠FGE+∠EFG = 180°

=> 90°+∠EFG = 180° (from (4))

=> ∠EFG = 180° -90°

=> ∠EFG = 90°

Therefore, ∠EFG = 90°

Answer:-

The measure of ∠EFG = 90°

Used formulae:-

→ If two parallel lines Intersected by a transversal then The interior angles on the same side to the transversal are supplementary.

→ The sum of all the three angles in a triangle is 180°