What are the angles in a 30-60-90 triangle?

In a 30-60-90 triangle, the measure of the angles is defined as 30 degrees, 60 degrees, and 90 degrees. This specific triangle is a right triangle where the angles are in a fixed ratio. The 30-degree angle is the smallest, the 60-degree angle is the next largest, and the 90-degree angle is the right angle, which is a defining characteristic of right triangles. The side lengths in a 30-60-90 triangle also follow a consistent ratio based on these angles, frequently expressed as 1 : √3 : 2. This triangle type is often used in geometry, trigonometry, and various applications in mathematics and science.

The other choices do not reflect the characteristics of a 30-60-90 triangle. For example, the alternative angles presented in the choices are either those from an isosceles right triangle or an equilateral triangle, or they simply do not constitute valid angle measures for any type of triangle. Hence, the correct choice accurately captures the defining features of the 30-60-90 triangle.