Question

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.

Answer 1

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°.