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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(52800)  (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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To learn about supplementary / complementary angles, read the lessons
- Angles basics
- HOW TO solve problems on supplementary, complementary or vertical angles - Examples
in this site.
Consider these lessons as your handbook, textbook, guide, tutorials and (free of charge) home teacher.
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@ewatrrr fixed her post after seeing my solution.
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