The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 17° 41' 13" , 96° 12' 10"

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. In this case, by adding the two given angles and subtracting from 180 degrees, we can find the third angle.

Angle Measurement

Angles can be measured in degrees, minutes, and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This system is particularly useful for precise measurements in trigonometry. When calculating the third angle, it is essential to ensure that all angles are in the same format, either converting everything to degrees or keeping them in degrees, minutes, and seconds.

Conversion of Angle Units

When working with angles expressed in degrees, minutes, and seconds, it may be necessary to convert these measurements into decimal degrees for easier calculations. The conversion involves taking the minutes and dividing by 60, and the seconds and dividing by 3600, then adding these values to the degree measure. This ensures accuracy when performing arithmetic operations, such as finding the third angle in a triangle.