Question

find the value of the variables in the given figure. x = y =

Explanation:

Step1: Find the value of \(x\)

Since \(6x + 2\) and \(7x-4\) are vertical - angles, they are equal.
So, \(6x + 2=7x - 4\).
Subtract \(6x\) from both sides: \(2=x - 4\).
Add \(4\) to both sides: \(x=6\).

Step2: Find the value of \(y\)

Since the two horizontal lines are parallel and the transversal cuts them, \(6x + 2\) and \(2y+6\) are corresponding - angles (and thus equal).
Substitute \(x = 6\) into \(6x+2\): \(6\times6 + 2=36 + 2=38\).
Set \(2y + 6=38\).
Subtract \(6\) from both sides: \(2y=32\).
Divide both sides by \(2\): \(y = 16\).

Answer:

\(x = 6\)
\(y = 16\)