Question

The measures of the acute angles of a right triangle have a ratio of 2:7. What is the measure of the smaller angle?

Answer 1

A triangle's interior angles must have a sum of 180 degrees. Hence the two acute angles must have a sum of 180-90=90 degrees.
Say that the angles have 2x and 7x length:
2x+7x=90
9x=90
x=10
Hence the acute angles have degrees 2*10=20, 7*10=70.
The smaller angle is 20 degrees.