Above ground electric wires and transformers are mounted on utility poles. a support cable, called a guy wire, is sometimes attached to give the pole stability. if the guy wire makes an angle of 60 degrees with the ground, what is the measure of the angle formed by the guy wire and the pole? assume that the ground is level.

The angle measure is 30 degrees.

Drawing out an image, the angle the is between the ground at the hypotenuse (the slanted guy wire), it creates a triangle with the utility pole that was already on the side. The angle between the utility pole and the ground is obviously 90 degrees because it is assumed to be at a straight standing stance.
Normally these two given angles would be added and then subtracted from 180 degrees (the law of Sum of Angles in a Triangle).
60 + 90 = 150   ...   180 - 150 = 30
Also, this can be supported by the 30-60-90 Theorem, which states that if a triangle contains 2 of the 3 angles, the other angle will be the missing one.