SOLUTION: One-fifth of the supplement of an angle is 9 degrees less than twice the complement of the angle. Find the measure of the supplement of the angle in degrees.

Question 1173619: One-fifth of the supplement of an angle is 9 degrees less than twice the complement of the angle. Find the measure of the supplement of the angle in degrees.
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi,
One-fifth of the supplement of an angle(x) is 9 degrees less than twice the complement of the angle(x).
Letting x represent the angle
Write as You Read:
Hitting the = sign at the 'is' as is usually the case
(1/5)(180° -x)= -9 + 2(90°-x)
(180° -x)= -45 + 10(90°-x)
180-x = -45 + 900- 10x
9x = 665
x = 75°
checking our answer:
(1/5)(180° -x)= -9 + 2(90°-x)
(1/5)(180° -75)= -9 + 2(90°-75)
21 = -9 + 30 checks.
Wish You the Best in your Studies.

Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.

            The solution by @ewatrrr is INCORRECT.   She READ the problem incorrectly -

            THERFORE, her first equation is incorrect, producing errors to the very end.

            I came to bring you the correct solution.

Solution

Let x be the angle measure in degrees. Then the supplement is (180-x); one-fifth of the supplement is and the complement is (90-x) degrees. THEREFORE, your equation is = 2*(90-x) - 9 Multiply both sides by 5 and simplify 180 - x = 10*(90-x) - 45 180 - x = 900 - 10x - 45 10x - x = 900 - 45 - 180 9x = 675 x = 675/9 = 75. ANSWER. The angle is 75 degrees. CHECK. Supplement is 105 degrees. One-fifth of supplement is 105/5 = 21 degrees; complement is 15 degrees and twice the complement is 30 degrees. Finally, 21 degrees is 9 degrees less than 30 degrees. ! Correct !

Solved.

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. . . . . . . .

@ewatrrr fixed her post after seeing my solution.

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