If angle y and angle x form vertical angles, then they ARE vertical angles. Vertical angles have the SAME degree measure. If angle y forms a straight line with the 80 degree angle and the 60 degree angle, this means that adding angle y, the 80 degree angle, and the 60 degree angle gives you a straight line. A line is 180 degrees. So, angle y's measure=180-(80+60). Since measure of angle x equals measure of angle y, the equation is m<x=180-(80+60).
Let's solve. m<x=180-(80+60). m<x=180-140. m<x=40 degrees.
Answer: m<x=180-(80+60); m<x=40 (degrees)