SOLUTION: The measures of two supplementary angles are in the ratio 2:3. Find their measures.

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Question 214210This question is from textbook Prentice Hall Mathematics Geometry
: The measures of two supplementary angles are in the ratio 2:3. Find their measures. This question is from textbook Prentice Hall Mathematics Geometry

Answer by drj(1380) About Me  (Show Source):
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The measures of two supplementary angles are in the ratio 2:3. Find their measures.

Step 1. Let 2x be one angle and 3x be the other angle. The ratio of these two angles is 2x/3x=2/3 as given on the problem.

Step 2. The two angles must add up to 180 degrees by definition.

Step 3. Then 2x+3x=180 or 5x=180 which implies that x=36. 2x=72 and 3x=108

Step 4. The angles are then 72 degrees and 108 degrees. Note the two angles add up to 180 and their ratio is 72/108=2/3 satisfying the problem statement.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J