Question

Can you please help me find the value of x and y while l is parallel to m.

Answer 1

Answer-

The values of x and y are 13 and 24, respectively.

Solution-

From the attachment, l and m are parallel lines and

$\Rightarrow (5x-8)+(4y+27)=180$

$\Rightarrow 5x+4y=161$    ---------------------1

As, when a traversal line intersects two parallel lines, same-side interior angles are supplementary, or they add up to 180 degrees.

$\Rightarrow (7x-31)+63=4y+27$

$\Rightarrow 7x-4y=-5$     ---------------------2

As, an exterior angle is equal to the sum of the opposite interior angles.

Adding equation 1 and 2, we get,

$\Rightarrow 5x+4y+7x-4y=161-5$  

$\Rightarrow 12x=156$  

$\Rightarrow x=13$  

Putting the value of x in equation 1, we get

$\Rightarrow y=24$