Question

line m is parallel to line n. the lines are cut by transversals y and z. what is the value of x?

Explanation:

Step1: Use corresponding - angle property

Since line $m$ is parallel to line $n$, the angle adjacent to the $110^{\circ}$ angle and the $60^{\circ}$ angle and the $4x^{\circ}$ angle are related. The adjacent - angle to the $110^{\circ}$ angle is $180 - 110=70^{\circ}$ (linear - pair of angles).

Step2: Set up an equation

The sum of the angles around the intersection point of the transversals and the parallel lines gives us the equation $4x+70 + 60=180$ (angles on a straight - line sum to $180^{\circ}$).

Step3: Simplify the equation

$4x+130 = 180$.

Step4: Solve for $x$

Subtract 130 from both sides: $4x=180 - 130$, so $4x = 50$. Then divide both sides by 4: $x=\frac{50}{4}=12.5$.

Answer:

$12.5$