SOLUTION: The measures of two supplementary angles are in the ratio of 4:5. Find the number of degrees in the measure of the smaller angle.

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Question 227670: The measures of two supplementary angles are in the ratio of 4:5. Find the number of degrees in the measure of the smaller angle.
Answer by josmiceli(19441) About Me  (Show Source):
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Call the angles
a and b
given:
(1) a+%2B+b+=+180 degrees
(2) a%2Fb+=+4%2F5
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Multiply both sides of (2) by b
a+=+%284%2F5%29%2Ab
Substitute in (1)
a+%2B+b+=+180
%284%2F5%29%2Ab+%2B+b+=+180
Multiply both sides by 5
4b+%2B+5b+=+900
9b+=+900
b+=+100
and, since
a+%2B+b+=+180
a+%2B+100+=+180
a+=+80
The smaller angle is 80 degrees