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