A sundial has circular dial and a right triangle shaped piece, called a gnomon. One of the angles of the gnomon is 52° What is the measure of the smallest angle of the gnomon?

The three inside angles of a triangle need to equal 180°

In a right triangle one of the angles is 90°

This means the other two angles need to equal 180-90 90 degrees

You are given one of the angles of 52°, so subtract that from 90 to find the third angle.

90 - 52 = 38 degrees.

Answer: 38°