Question

1. if ( m parallel n ), ( m angle 6 = 4x + 7^{circ} ), and ( m angle 3 = 2x + 53^{circ} ), find the value of ( x ).

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), \(\angle3\) and \(\angle6\) are alternate interior angles. So \(m\angle3 = m\angle6\).

Step2: Set up the equation

We have \(4x + 7=2x + 53\).

Step3: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(4x-2x + 7=2x-2x + 53\), which simplifies to \(2x+7 = 53\).
Subtract \(7\) from both sides: \(2x+7 - 7=53 - 7\), so \(2x=46\).
Divide both sides by \(2\): \(x=\frac{46}{2}\).

Answer:

\(x = 23\)