Question

parallel lines e and f are cut by transversal b. what is the value of x? 1 5 25 37 (2x + 10)° (3x - 15)°

Explanation:

Step1: Use the property of alternate interior angles

Since lines \(e\) and \(f\) are parallel and cut by transversal \(b\), the alternate interior angles \((2x + 10)^{\circ}\) and \((3x-15)^{\circ}\) are equal. So, \(2x + 10=3x - 15\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation: \(2x+10-2x = 3x - 15-2x\), which simplifies to \(10=x - 15\).
Then add \(15\) to both sides: \(10 + 15=x-15 + 15\).

Answer:

\(x = 25\)