Find the measure of an angle such that the difference between the measures of its supplement and three times its compliment is 10 degrees

Question

This is a math question 

Answer 1

Remember that two complimentary angles equal 90 degrees and supplementary, 180.

 

If a + b = 90, then a = 180 - b, right?

 

(180 - a) - 3(90 - a) = 10

180 - a - 270 + 3a = 10

2a = 100

a = 50

 

So, if an angle is 50 degrees, its complement is 40 and its supplement is 130.

 

130 - 3(40) = 10

130 - 120 = 10

10 = 10

 

Yep, 50 degrees.