The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 29.6° , 49.7°

Verified step by step guidance

1. Start by recalling the Triangle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.
2. Identify the given angles of the triangle: 29.6° and 49.7°.
3. Add the measures of the two given angles: 29.6° + 49.7°.
4. Subtract the sum of the two given angles from 180° to find the measure of the third angle: 180° - (29.6° + 49.7°).
5. Simplify the expression to find the measure of the third angle.

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 29.6° and 49.7°, 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 the question about triangle angles, understanding complementary angles can help in broader trigonometric contexts, especially when dealing with right triangles. In this case, however, we focus on the sum of angles in a triangle rather than complementary relationships.

Angle Measurement

Angle measurement is typically expressed in degrees or radians. In this context, degrees are used to quantify the angles of the triangle. Understanding how to convert between degrees and radians can be useful in more advanced trigonometric applications, but for this problem, we simply need to work with the degree measures provided to find the third angle.