The hypotenuse of a right triangle measures 10 inches, and the side opposite to ∠θ, one of the non-right angles, is 5 inches long. The measure of ∠θ is

The measure of angle theta is 30 degrees.

This is a 30-60-90 triangle where the short leg is half that of the hypotenuse. The short leg is opposite the smallest angle 30 degrees.

You can use trig to find that

sin (angle) = opposite/hypotenuse

sin (theta) = 5/10

sin (theta) = 0.5

theta = arcsin (0.5)

theta = 30 degrees