# Answer to Question #14991 in Geometry for Abby

Question #14991

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.

Expert's answer

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°.

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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