Question

in the figure below, the lines are parallel, ( mangle7=(6x - 22)^{circ} ) and the ( mangle1=(4x + 20)^{circ} ), what is ( x=? )

Explanation:

Step1: Use the property of corresponding angles

Since the lines are parallel, \(m\angle1 = m\angle7\) (corresponding angles).
So, \(6x - 22=4x + 20\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(6x-4x - 22=4x-4x + 20\), which simplifies to \(2x-22 = 20\).
Add \(22\) to both sides: \(2x-22 + 22=20 + 22\), so \(2x=42\).
Divide both sides by \(2\): \(x=\frac{42}{2}\).

Answer:

\(x = 21\)