Finding the measure of an angle

find the measure of an angle such that the sum of the measure of its complement and its supplement is 160 degrees.

x - measure of the angle
90-x - measure of the complement
180-x - measure of the supplement

90-x+180-x=160
2x=180+90-160
2x=110
x=55

proof

complement 90-55 = 35
supplement 180-55 = 125
35+125=160


complement

The complement of an angle is 90 - the angle.
The supplement of an angle is 180 - the angle

Let the angle = A
90 - A + 180 - A = 160
270 - 2A = 160
270 - 160 = 2A
110 = 2A
A = 55

Check:
90 - 55 = 35
180 - 55 = 125
125 + 35 = 160

90-x+180-x=160
270-2x=160
-2x=-110
2x=110
x=55

A+comp = 90

A+suppl=180

comp+suppl = 270-2A=160

2A=110

A=55 degrees

add or subtract 90 degrees from it can't remember which is which though sorry