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Question 476475: The degree measure of an angle and its supplement are consecutive odd integers. Find the measure of each angle.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let D represent an odd integer. Then the next consecutive odd integer has to be +2 above that number. (Example, since 3 is an odd integer, the next consecutive odd integer has to be 3 + 2 = 5.)
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We know that the two angles we are to find are supplementary -- meaning that when added together their sum is 180 degrees.
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So we can say that:
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D + (D + 2) = 180
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The parentheses can be removed:
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D + D + 2 = 180
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Subtract 2 from both sides of the equation:
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D + D = 178
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Add the two terms on the left side:
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2D = 178
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and solve for D by dividing both sides of the equation by 2:
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D = 89
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So we know that the measure of one of the two angles is 89 degrees. The other angle is +2 more so that it is 91 degrees.
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These two angle measures satisfy the problem. They are consecutive odd integers and their sum is 180 degrees so they are also supplementary.
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Hope this helps you to understand how to do this problem.
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