Question

In the figure AB is parallel to CD. EG and FG are bisectors of angle BEF and angle DFE respectively. The measure of angle FGE is:

a) half of a right angle

b) 60 degrees

c) half of a straight angle

d) 180 degrees


Please help me solve this problem, it's really urgent ❤️​

Answer 1

Given :

• AB // CD

• EG , FG are bisectors of angle BEF , DEF

• Measure of angle FGE = ?

$\large \: here...$

Line FR is transversal of lines

• AB and CD

$\large \sf \: since.. \\ \\ \tt \large \: these \: \: are \: \: parellal \: \: lines$

So angle ,

• BEF = DEF = 90°

$\large \rm \: as \: \: angles \: \: are \: \: bsected \\ \\ \large \implies \rm\: \angle \: bef = \angle \: def = \frac{90}{2} \\ \\ \large \mapsto \: measure \: \: of \: angles = 45 \degree$

So angle ,

• GEF = GFE = 45°

$\\ \large \sf \: in \: \triangle \: \: gef : \\ \\ \large \sf \rightarrow \: \angle gef + \angle gfe + \angle g = 180 \degree$

$\large \rm \underline{ (\underline{ \: angle \: \: sum \: \: property )}}$

$\large \sf \implies \: 45 \degree + 45 \degree + \angle g = 180 \degree \\ \\ \large \sf \implies \: 90\degree + \angle g = 180 \degree \\ \\ \large \sf \implies \: \angle g = 180 \degree - 90 \degree$

$\large \underline{ \boxed{ \therefore \rm \: \angle g = 90 \degree}}$

Angles of straight line = 180°

• half of 180°

$\\ \large \: = \dfrac{180 \degree}{2}$

= 90°

• Angle G = 90°

So,answer = Option :

d) Half of a straight line

Answer 2

Given: AB is parallel to CD. EG and FG are bisectors of angle BEF and angle DFE

To find:  The measure of angle FGE that is angle G.

Solution:

As visible in the figure, the straight line FR is the transversal of lines

AB and CD.

As these two lines, AB and CD are parallel to each other,

Therefore, BEF=DEF= 90 degrees.

Now, GEF=GFE because of FG AND EG being the angle bisectors.

In triangle GEF

We will apply the property of the sum of all the angles in a triangle is 180 degrees.

Since DFE and BEF are right-angled triangles, Angle GEF and angle GFE will each be 45 degrees.

So, GEF+GFE+Angle G= 180 degrees

45+45+G=180 degrees.

G=180-90

G=90

So G is half of a straight angle which is 180/2= 90 degrees.

The measure of angle FGE is 90 degrees which is C). half of a straight angle.