SOLUTION: twice the supplement of an angle added to three time the complement of the angle is eight times the complement. find the supplement of the angle to the nearest 10th
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Question 225076: twice the supplement of an angle added to three time the complement of the angle is eight times the complement. find the supplement of the angle to the nearest 10th Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! Twice the supplement of an angle added to three times the complement of the angle is eight times the complement. Find the supplement of the angle to the nearest 10th.
Step 1. Supplementary angles means two angles add up to 180 degrees.
Step 2. Complementary angles means two angles add up to 90 degrees.
Step 3. Let x be the angle.
Step 4. Let 180x be the supplement of the angle x.
Step 5. Let 90-x be the complement of the angle x.
Step 6. Let 2(180-x) be twice the supplement.
Step 7. Let 3(90-x) be three times the complement.
Step 8. Let 8(90-x) be eight times the complement.
Step 9. Then, 2(180-x)+3(90-x)=8(90-x) since twice the supplement of an angle added to three times the complement of the angle is eight times the complement.
Step 10. Solving the equation in Step 9 leads to the following steps:
Add 8x-630 to both sides of the equation
Divide by 3 to both sides of the equation
Then, and
Check if equation in Step 9 is true...2(150)+3(60)=8*60 or 300+180=480 which is a true statement.
Step 7. ANSWER: The supplementary angle is 150 degrees. Also, the angle is 30 degrees and its complementary angle is 60 degrees
I hope the above steps and explanation were helpful.
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