Question

FG ∥ CB, A ∈ FG, D ∈ AB, E ∈ AC

Answer 1

Answer:

The value of x is $31^{\circ}$.

Step-by-step explanation:

Please look at the figure attached to get more clear solution.

We have given:

FG||CB

And the line that cut the parallel line is transversal so, here BA is transversal

And alternate interior angles on transverse line are equal

So, ∠1=∠4

And ∠4=$28^{\circ}$

Hence,  ∠1=∠4=$28^{\circ}$

And On FG the sum of angles will be $180^{\circ}$

∠3+∠2+∠1=$180^{\circ}$

$90^{\circ}$+∠2+$28^{\circ}$=$180^{\circ}$

Hence, ∠2=$62^{\circ}$

Now, we know that the sum of interior angles is equal to the exterior angle:

Therefore, ∠2+∠5=∠6+∠7

$62^{\circ}+3x=x+4x$

On simplification we get:

$2x=62^{\circ}$

$x=31^{\circ}$

Hence, the value of x is $31^{\circ}$.