Question

solve for x.

x =

Explanation:

Step1: Identify the relationship

The two angles \((4x - 10)^\circ\) and \((3x + 25)^\circ\) are alternate interior angles because the lines \(JL\) and \(LM\) (wait, actually \(JK\) and \(LM\) are parallel, and the transversal is \(HI\)). So alternate interior angles are equal. So we set up the equation: \(4x - 10 = 3x + 25\).

Step2: Solve for x

Subtract \(3x\) from both sides: \(4x - 3x - 10 = 3x - 3x + 25\) which simplifies to \(x - 10 = 25\). Then add 10 to both sides: \(x - 10 + 10 = 25 + 10\), so \(x = 35\).

Answer:

\(35\)