Question

find the values of x and y.
diagram of two intersecting lines with angles labeled 4x°, (7y - 12)°, (6y + 8)°, (6x - 26)°
x = □
y = □

Explanation:

Step1: Use vertical angles property

Vertical angles are equal, so \(4x = 6x - 26\) and \(7y - 12 = 6y + 8\).

Step2: Solve for \(x\)

\(4x = 6x - 26\)
Subtract \(4x\) from both sides: \(0 = 2x - 26\)
Add 26 to both sides: \(26 = 2x\)
Divide by 2: \(x = 13\)

Step3: Solve for \(y\)

\(7y - 12 = 6y + 8\)
Subtract \(6y\) from both sides: \(y - 12 = 8\)
Add 12 to both sides: \(y = 20\)

Answer:

\(x = 13\)
\(y = 20\)