Question

1. m n 150° (3x - 15)°

Explanation:

Step1: Identify supplementary angles

Since lines \(m\) and \(n\) are parallel, \(150^\circ\) and \((3x-15)^\circ\) are same-side interior angles, so they are supplementary (sum to \(180^\circ\)).
$$150 + (3x - 15) = 180$$

Step2: Simplify the left side

Combine constant terms.
$$3x + 135 = 180$$

Step3: Isolate the variable term

Subtract 135 from both sides.
$$3x = 180 - 135$$
$$3x = 45$$

Step4: Solve for \(x\)

Divide both sides by 3.
$$x = \frac{45}{3}$$

Answer:

\(x = 15\)