Question

The measures of two angles 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

`75/2` and `45/2`

Explanation:

The idea that the values are angles is a "red herring"; it is irrelevant to the question.

Let the two values ("angles") be `A` and `B` with `A > B`

We are told
`color(white)("XXX")A/B=5/3`
`color(white)("XXXXXX") rarr A=5/3B`
and
`color(white)("XXX")A=30+(A-B)/2`

`color(white)("XXXXXX") rarr 2A=60+A-B`

`color(white)("XXXXXX") rarr A=60-B`

So
`color(white)("XXX")5/3B=60-B`

`color(white)("XXXXXX")rarr8/3B=60`

`color(white)("XXXXXX")rarr B=(60xx3)/8=45/2`

and
`color(white)("XXX")A=5/3B=(5xx45)/(3xx2) = 75/2`