What is the ratio of the given angles in a triangle that respectively measure 30°, 60°, and 90°?

To determine the ratio of the angles in a triangle that measure 30°, 60°, and 90°, we look at the values of the angles themselves.

First, we can express the angles in a simplified form to analyze their relationship. The angles are 30°, 60°, and 90°. To find the ratio, we can simply write these angles as:

30:60:90

Next, we can reduce the angles to their simplest form to understand the ratio. Each of the angles can be divided by 30:

30 ÷ 30 = 1

60 ÷ 30 = 2

90 ÷ 30 = 3

This gives us the ratio 1:2:3.

This ratio uniquely characterizes the angles in the triangle, reflecting their relative measures. It indicates that for every unit represented by 30°, there are two units represented by 60° and three units represented by 90°. Therefore, the correct answer accurately represents the ratio of the angles in the triangle.