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


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Answer 1

Answer:

90

Step-by-step explanation:

angle BEG and angle DGE are add up-to 180

same side of a transversal line

so angle BEG+angle DGE=180

angle FEG= (1/2)angle BEG

same way FGE =(1/2)DGE

so angles(FGE+FEG)= (1/2)(180)= 90

so angle EFG = 180-(FGE+FEG)

=90

Answer 2

Answer:

90°

Step-by-step explanation:

Let's say the required angle be x.

Given that,

∠ BEF = ∠ GEF

∠ EGF = ∠ FGD

since EF and FG are bisectors.

Now, by using property of co interior angles,

⇒ ∠ BEF + ∠ GEF + ∠ EGF + ∠ FGD = 180°

⇒ ∠ GEF + ∠ GEF + ∠ EGF + ∠ EGF = 180°

⇒ 2 ( ∠ GEF + ∠ EGF ) = 180°

⇒ ∠ GEF + ∠ EGF = 90° _____(1)

Now apply angle sum property in ∆ GEF

⇒ ∠ GEF + ∠ EGF + ∠ EFG = 180°

Using equation (1)

⇒ 90° + x = 180°

⇒ x = 180° - 90°

⇒ x = 90°

So the required angle is of 90°.