9514 1404 393
Answer:
Explanation:
The angles of a linear pair are supplementary. That is, they total 180°. The angle marked x° and the one marked 72° are a linear pair:
x° +72° = 180°
x = 180 -72 = 108 . . . . . . . divide by °, subtract 72
__
Vertical angles are congruent. Angles y° and 72° are vertical angles, so ...
y = 72
__
Angles z° and 72° together make a right, which has a measure of 90°.
z° +72° = 90°
z = 90 -72 = 18 . . . . . . . divide by °, subtract 72
__
(x, y, z) = (108, 72, 18)
_____
Additional comment
Angles 72° and x° form a linear pair, as do angles x° and y°. That is, angles 72° and y° are both supplementary to angle x°. Angles that are supplementary to the same angle are congruent. This will be the case for any vertical angles: they are supplementary to the same angle.