The Measures of two angels are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. What is the measure of each angle.
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Expert's answer
2012-09-25T12:14:49-0400
Let a be the smaller angle and b be the larger angle. Then
5a = 3b b-30 = (b-a)/2
Let's solve this system.
5a = 3b ==> a = 3b/5 b-30 = (b-3b/5)/2 b-30 = b/2 - 3b/10 4b/5 - 30 = 0 b = 37.5 a = 3*37.5/5 = 22.5.
So, the smaller angle has measure of 22.5° and the larger one 37.5°.
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