SOLUTION: The ratio of two complementary angles is 17:13. What is the measure of the smaller angle?

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Question 1113926: The ratio of two complementary angles is 17:13.
What is the measure of the smaller angle?
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

let’s two complementary angles be alpha and beta and let’s alpha%3Ebeta
if the ratio of two complementary angles is 17%3A13 we have
alpha%3Abeta=17%3A13…eq.1
alpha%2Bbeta=90…eq.2
From eq.1 we have 13alpha=17beta ->alpha=17beta%2F13
Substitute it in eq.2
alpha%2Bbeta=90…eq.2
+17beta%2F13+%2Bbeta=90
+17beta+%2B13beta=90%2A13
+30beta=90%2A13
+beta=%2890%2A13%29%2F30
+beta=3%2A13
+beta=39->is the measure of the smaller angle

Check:
Find alpha first
alpha%2B39=90
alpha=90-39
alpha=51
alpha%3Abeta=17%3A13…eq.1
51%3A39=17%3A13
51%2A13=39%2A17
663=663