The measures of the acute angles of a triangle are in the ratio 1:5. What is the measure of each acute angle of the triangle?

Question

I'm not sure how to solve this, or what a ratio means.

Answer 1

This problem cannot be solved without additional information.  Most likely, the triangle was a right triangle.

In that case the sum of the two acute angles is  90 degrees.   Let the smaller of the two acute angles have measure x.   Then the measure of the larger one is 5x.    

 

This leads to the equation   x + 5x = 90.        Solution is  x = 15. 

So the smaller angle has measure 15, the larger has measure 75.