Question

Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure of one of the four angles formed is 72 degrees, what are the measures of the other three angles? Explain your answer.

Answer 1

So base on your question that ask to find the other measurements of the angles that is formed by 2 straight length of wire where as the measurement of one angle is 72 degrees. The wires has a pair of adjacent angles and each of them has 180 degree in total, so the measurement is 108,72,108

Answer 2

We have
angle 1=$72 degrees$

see the attached picture to better understand the problem

we know that
Vertical angles are congruent
$angle1=angle3 \\ angle2=angle4$

and

adjacent angles are supplementary
$angle2+angle1=180 \\ angle3+angle4=180$

if the measure of one of the angles is $72$ degrees and straight lines equal $180$ degrees you have to
subtract $72$ from $180$
so
$angle 2=180-72 \\ angle 2=108 degrees$

therefore
$angle 3=amgle 1 \\ angle 3=72 degrees$

$angle 4=amgle 2 \\ angle 4=108 degrees$

the answer is

the measures of the other three angles are
$108, 108 and 72 degrees$