SOLUTION: the measure of two complementary angles have a ratio of 2 : 7. what is the measure of the smaller angle

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Question 578189: the measure of two complementary angles have a ratio of 2 : 7. what is the measure of the smaller angle
Answer by josmiceli(19441) About Me  (Show Source):
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Complementary means the angle add up to 90 degrees
Let the angles be a and b
given:
(1) +a+%2B+b+=+90+
(2) +a%2Fb+=+2%2F7+
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Multiply both sides of (2) by +7b+
(2) +7a+=+2b++
and
(1) +b+=+90+-+a+
Substitute this into (2)
(2) +7a+=+2%2A%28+90+-+a+%29+
(2) +7a+=+180+-+2a+
(2) +9a+=+180+
(2) +a+=+20+
and
+b+=+90+-+a+
+b+=+70+
The smaller angle is 20 degrees