Question

1. if ( p parallel q ), ( m angle 2 = 5x - 5^{circ} ), and ( m angle 7 = 2x + 10^{circ} ). find ( x ).

Explanation:

Step1: Use the property of alternate exterior angles

When \(p\parallel q\), \(\angle2\) and \(\angle7\) are alternate exterior angles. So \(m\angle2 = m\angle7\).

Step2: Set up the equation

Since \(m\angle2=5x - 5^{\circ}\) and \(m\angle7=2x + 10^{\circ}\), we have the equation \(5x-5=2x + 10\).

Step3: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(5x-2x-5=2x-2x + 10\), which simplifies to \(3x-5=10\).
Add \(5\) to both sides: \(3x-5 + 5=10+5\), so \(3x=15\).
Divide both sides by \(3\): \(x=\frac{15}{3}\).

Answer:

\(x = 5\)