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"

검증된 단계별 안내

Recall that the sum of the interior angles of any triangle is always \(180^\circ\).

Convert the given angles from degrees, minutes, and seconds into a consistent format to make addition easier. Remember that 1 degree = 60 minutes and 1 minute = 60 seconds.

Add the two given angles together by separately adding degrees, minutes, and seconds. If the seconds sum to 60 or more, convert the excess into minutes. Similarly, if the minutes sum to 60 or more, convert the excess into degrees.

Subtract the sum of the two given angles from \(180^\circ\) to find the measure of the third angle. Perform this subtraction carefully, borrowing minutes or seconds if necessary.

Express the result in degrees, minutes, and seconds format to give the measure of the third angle.

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Angle Measurement in Degrees, Minutes, and Seconds

Angles can be expressed in degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. Understanding this notation is essential for accurately adding or subtracting angles given in this format.

Sum of Angles in a Triangle

The sum of the interior angles in any triangle is always 180 degrees. This fundamental property allows us to find the unknown angle when the other two angles are known by subtracting their sum from 180°.

Conversion and Subtraction of Angles

When subtracting angles expressed in degrees, minutes, and seconds, it may be necessary to convert between these units to perform the calculation correctly. Borrowing from degrees to minutes or minutes to seconds ensures accurate subtraction.

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"