<55 and <(3x + 4) are complimentary which means they have the same measure. Set them to equal:
55 = 3x + 4
Subtract 4
51 = 3x
Divide by 3
17 = x
Now to solve for y, add 55 and 8y - 1 for they are supplementary and add up to 180.
55 + 8y - 1 = 180
54 + 8y = 180
Subtract by 54
8y = 126
y = 15.75