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Question 283601: Can you please help me understand and solve this problem: One angle is 15 degrees less than twice another angle. If the angles are complementary find each angle
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! If angles are complementary, then the sum to 90 degrees.
We have two angles, say 'x' and 'y'.
We know from the problem statement they are complementary, so
x+y=90
Given this equation, we can see that it is easier to define them as:
'x' and '90-x'.
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That leaves us with only one unknown to solve.
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In algebra, we'd say:
x = x
y = 90-x
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We also are told one angle is 15 less than twice the other. So if we add 15 to one of the angles, it will equal twice the other angle.
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y+15 = 2x
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Which means
y = 2x - 15
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Returning to the objective equation:
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x + y = 90
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Substitute y = 2x-15
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x + 2x-15 = 90
3x -15 = 90
3x = 105
x = 35
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x + y = 90
y = 90 -35
y = 55
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Check to see if these values satisfy the other problem statement:
y + 15 = 2x
y+15 = 55+15 = 70
2x = 2*35 = 70
Correct.
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Answer:
The two angles are: 35 and 55.
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Done.
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