Question

Find the value of y in the diagram below

Answer 1

`we \: can \: tell \: that \\ 1. \: \: 13x - 26 = 7x + 16 \\ 2. \: \: 7 x + 16 + 9y + 7 = 180\\ from \: 1. \\ 6x = 42 \: so \: x = 7 \\ from \: 2. \\ y = 12`

Answer 2

x=7 and y=12.

Explanation:

If two lines intersect each other then vertical opposite angles are equal.

`13x-26=7x+16`

`13x-7x=26+16`

`6x=42`

Divide both sides by 6.

`x=7`

The value of x is 7.

`(7x+16)^\circ=(7\cdot 7+16)^\circ=(49+16)^\circ=65^\circ`

Same side interior angles are supplementary angles.

`(7x+16)^\circ+(9y+7)^\circ=180^\circ`

`65^\circ+(9y+7)^\circ=180^\circ`

`(9y+7)^\circ=180^\circ-65^\circ`

`(9y+7)^\circ=115^\circ`

On further simplification we get

`9y+7=115`

`9y=115-7`

`9y=108`

Divide both sides by 9.

`y=12`

Therefore, the value of y is 12.