Question

find the value of x? ​

Answer 1

Using corresponding angle theorem (or alternate opposite angle theoum) of two parallel lines, we see
4x and 5x are linear pair of angles
I.e.
4x + 5x = 180
=> 9x = 180
=> x = 20

Answer 2

Let us,

Name the points as shown in the figure.

Given :

$\angle \: PEF = 4x \\ \angle \: BFY = 5x$

To find :

$•Value \: of \: x$

Solution :

$\because \: line \: \ell \parallel \: line \:m \: and \: line \:n \: is \: \\ their \: transversal \\ \therefore \angle \: BFY = \angle \: FEQ \\ </p><p>- ( Corresponding \: angles ) \\ \therefore \boxed{\angle \: FEQ \: = 5x}</p><p>$

$\therefore \angle \:FEP + \angle \:FEQ = 180 \degree \\ - ( Angles \: in \: linear \: pair ) \\ \\ \therefore \: 4x + 5x = 180 \degree \\ \\ \therefore \: 9x = 180 \degree \\ \\ \therefore \: x = \frac{180}{9 } \\ \\ \therefore \boxed{\: x = 20 \degree}$

Verification :

$1 ) \: \angle \: PEF = 4x \\ = 4 \: (20) \\ = 80 \degree \\ \\ 2) \: \angle \: BFY = 5x \\ = 5 \: (20) \\ = 100 \degree$

[ Note : Refer the figure ]