Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of alternate interior angles

Since \( m\parallel n \), the angles \( (9x - 8)^{\circ} \) and \( (4x + 22)^{\circ} \) are equal. So, \( 9x-8=4x + 22 \).

Step2: Solve the equation for \( x \)

Subtract \( 4x \) from both sides: \( 9x-4x-8=4x-4x + 22 \), which simplifies to \( 5x-8=22 \).
Add \( 8 \) to both sides: \( 5x-8 + 8=22+8 \), so \( 5x=30 \).
Divide both sides by \( 5 \): \( x=\frac{30}{5}=6 \).

Answer:

\( x = 6 \)