Question

If an angle is 18 degrees less than twice its complement, how do you find the ratio of the angle to its complement?

Answer 1

Let's call the angle we seek `alpha`

Then the complement is defined as `90^o-alpha`
And twice the complement would then be:
`2*(90^o-alpha)=180^o-2alpha`

So the equation turns into:
`alpha=(180^o-2alpha)-18^o=162^o-2alpha->`
Add `2alpha` to both sides, later divide by `3`:
`3alpha=162^o->alpha=54^o`

Check your answer :

If `alpha=54^o->`complement=`36^o`
Twice complement=`72^o`
Difference=`18^o` Check!