Question

Find the value of x.

Answer 1

From the given figure,

4x and 2y +x are supplementary angles

Supplementary angles are added upto 180 degrees

So 4x + 2y +x = 180

5x + 2y = 180 -------------> equation 1

4x and 2y-x are vertical angles so they are equal

4x = 2y - x

Keep all the x and y terms on left hand side

add x and subtract 2y on both sides

5x - 2y =0 -------- > equation 2

Add equations 1 and 2

5x + 2y = 180

5x - 2y = 0

10 x = 180 ( divide by 10 on both sides)

x= 18