The angles measuring 72 and 4y - 8 are vertical angles.
Vertical angles are congruent. Their measures are equal.
4y - 8 = 72
4y = 80
y = 20
The angles with measures 72 and 10x + 8 are a linear pair. They are supplementary meaning that heir measures add up to 180.
10x + 8 + 72 = 180
10x + 80 = 180
10x = 100
x = 10