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___?​

Answer 1

Answer:

Answer: 90

Step-by-step explanation:

let angles XEA = BEG = EGC = DGY = X

let angles XEB = AEG = EGD = CGY = Y

Then FEG = X/2

and FGE = Y/2

As sum of angles in a triangle =180

FEG + FGE + EFG =180

X/2 + Y/2 + EFG = 180

Therefore angle EFG = 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°.