Angel question/ Algebra?

Question

find the measure of an angle such that the difference between the measures of its supplement and three times its complement is 10*

Answer 1

Let's use the variable x to represent the measurement of the angle we are trying to find. Then its supplement is 180 - x. Its complement is 90 - x, so three times its complement would be 3(90-x) or if you go ahead and multiply to remove the parentheses then three times its complement is 270 - 3x. Therefore, the difference between the measures of its supplement and three times its complement would be (180 - x) - (270 - 3x). 180 - 270 is -90. -x - -3x is 2x. So, (180 - x) - (270 - 3x) = 2x - 90 which we are told equals 10. So now we know that 2x - 90 = 10. Add 90 to both sides and you have 2x = 100. Finally divide both sides by 2 and you get the answer, x = 50!

Let's check it. The supplement of 50 is 180 - 50 (which is 130). The complement of 50 is 90 - 50 (which is 40) so three times the complement of 50 is 3 times 40 (which is 120). The difference between them (130 - 120) is 10 so the answer 50 is correct.

Answer 2

Supplementary angles add up to 180 degrees, so if...
Angle = A
Supplement = 180 - A

Complementarty angles add up to 90 degrees, so if...
Angle = A
Complement = 90 - A

Difference of Supplement and three times the complement is 10, so...
Supplement = 180 - A
Three times the complement = 3(90 - A) = 270 - 3A
(180 - A) - (270 - 3A) = 10
180 - A - 270 + 3A = 10
-90 + 2A = 10
2A = 100
A = 50 degrees

Hope I helped!
10 points best answer?

Answer 3

lets say that the angle is x. x+y=180....x+z=90....y-3z=10......y-z=90...-4z=-80.......z=20.... x+20=90....x=70!!! Yay! so we have the answer, now let me explain. We know that the supplementary angles add up to 180. Lets name the angle supplementary to x, y. The angle complementary (sum=90) lets call z. We know that the suplementary, y, minus three times the complementary, 3z, is 10. Then, subtractting the 1st 2 equations from one another (linear systems) you get y-90... simplify... x=70!!!