Two angles are supplements if their sum is 180 degrees. the measure of one angle is seven-fifths the measure of its supplement. what is the measure of the smaller angle?

The measure of the smaller angle is 75 degrees.

Given:
Angle 1 + Angle 2 = 180 degrees
Angle 1 = x
Angle 2 = 7/5 * x

x + 7/5 * x = 180
x + 7x/5 = 180
5(x + 7x/5) = 5(180)
5x + 7x = 900
12x = 900
x = 900/12
x = 75 degrees. Angle 1.

Angle 2 = 7/5 * x = 7/5 * 75 = (7 * 75)/5 = 525/5 = 105 degrees

To check:
Angle 1 + Angle 2 = 180 degrees
75 deg + 105 deg = 180 deg
180 deg = 180 deg

So the 2 angles are x and y

'their sum is 180'
x+y=180

one is 7/5 of its supplement
the supplement is the angle that, when added to it, equals 180 (x+y=180, x is the supplement of y and y is the supplement of x)
let's say that the first one is x
x is 7/5 of y
'of' means multiply
x=7/5 times y
x=7y/5
subsitute
x+y=180
subsitute 7y/5  for x
7y/5+y=180
convert y to 5y/5
7y/5+5y/5=180
add
7y/5+5y/5=(7y+5y)/5=12y/5
12y/5=180
multiply both sides by 5
12y=900
divide both sides by 12
y=75
x+y=180
x+75=180
subtract 75 from both sides
x=105

the smaller angle is 75  degrees

(1/x + 1)^2 + 6 (1/x + 1) +5