Answer: 60
x = 10, y = 50
==================================================
Step-by-step explanation:
The 85 degree angle up top and the (3x+55) degree angle at the bottom are one pair of vertical angles.
Vertical angles are always equal in measure.
3x+55 = 85
3x = 85-55
3x = 30
x = 30/3
x = 10
The other pair of vertical angles are the 95 and (2y-5). Vertical angles don't have to align vertically. They simply need to be opposite one another in the X configuration as shown.
2y-5 = 95
2y = 95+5
2y = 100
y = 100/2
y = 50
We can now add up the values of x and y
x+y = 10+50 = 60 which is the final answer.
-------------
Another approach:
The angles 95 and (3x+55) form a straight angle of 180 degrees.
The angles are supplementary so they must add to 180.
95+(3x+55) = 180
3x+150 = 180
3x = 180-150
3x = 30
x = 30/3
x = 10
We arrive at the same x value found earlier.
Use similar logic to add up the other pair of supplementary angles to solve for y.
85 + (2y-5) = 180
2y+80 = 180
2y = 180-80
2y = 100
y = 100/2
y = 50
We arrive at the same y value as earlier.
So we'll arrive at x+y = 10+50 = 60 as the final answer.