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Question 462209: If an angle is 42 degrees less than its supplement, find each angle.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! If an angle is 42 degrees less than its supplement, find each angle.
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Two angles are supplements if their measures add to 180 degrees.
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Let
x = the measure of the first angle
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The second angle is 42 less than x. An algebraic expression for the second angle is x-42 since the second angle is 42 less than the first angle.
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We also know that the two angles are a supplementary pair. Their measures add up to 180 degrees. We can translate this English sentence into an equation:
x + (x-42) = 180
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Now we solve for x.
x + (x-42) = 180
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Combine like terms.
2x - 42 = 180
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Add 42 to both sides
2x = 180 + 42
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Combine like terms and divide both sides by 2.
2x = 222
x = 111
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The measure of the first angle is 111 degrees.
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We know that the second angle is 42 degrees less, so the second angle is 111 - 42 = 69 degrees.
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We see that these two angles are supplementary because 111 + 69 = 180.
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Hope this helps!
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Ms.Figgy
math.in.the.vortex
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