The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°

Key Concepts

Triangle Angle Sum Theorem

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. This fundamental principle allows us to determine the measure of an unknown angle when the measures of the other two angles are known. For example, if two angles measure 37° and 52°, we can find the third angle by subtracting their sum from 180°.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. While this concept is not directly applicable to finding the third angle in a triangle, understanding complementary angles can help in various trigonometric problems. In the context of triangles, it is important to distinguish between complementary angles and the angles that sum to 180 degrees.

Angle Measurement

Angle measurement is the process of determining the size of an angle in degrees or radians. In this problem, angles are given in degrees, which is a common unit for measuring angles in trigonometry. Understanding how to convert between degrees and radians, as well as how to manipulate angle measures, is essential for solving problems involving triangles and other geometric figures.