Question

Find the value of y in the diagram below

Answer 1

Answer:

x=7 and y=12.

Step-by-step 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.

Answer 2

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