Question

given: ( a parallel b ). ( angle 2 = 10x - 7 ) and ( angle 7 = 3x + 42 ). solve for ( x ).

Explanation:

Step1: Use the property of alternate exterior angles

Since \(a\parallel b\), \(\angle2\) and \(\angle7\) are alternate exterior angles. Alternate exterior angles are equal when two parallel lines are cut by a transversal. So, \(10x - 7=3x + 42\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(10x-3x - 7=3x-3x + 42\), which simplifies to \(7x-7 = 42\).
Add \(7\) to both sides: \(7x-7 + 7=42 + 7\), so \(7x=49\).
Divide both sides by \(7\): \(x=\frac{49}{7}\).

Answer:

\(7\)