The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 147° 12' , 30° 19'

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

Convert the given angles from degrees and minutes into a consistent format if needed, keeping degrees and minutes separate for easier calculation: $147^\circ 12'$ and $30^\circ 19'$.

Add the degrees parts of the two given angles: $147^\circ + 30^\circ$ and add the minutes parts: $12' + 19'$.

If the sum of the minutes is 60 or more, convert the excess minutes into degrees (since \$60'$ equals $1^\circ$) and add that to the degrees sum.

Subtract the total sum of the two given angles from $180^\circ$ to find the measure of the third angle, keeping track of degrees and minutes separately.

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Triangle Angle Sum Property

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

Conversion Between Degrees and Minutes

Angles can be expressed in degrees (°) and minutes ('). One degree equals 60 minutes. When performing addition or subtraction with angles, it is important to correctly convert and carry over between degrees and minutes to maintain accuracy.

Subtraction of Angles with Degrees and Minutes

To find the unknown angle, subtract the sum of the given angles from 180°. This requires careful subtraction of degrees and minutes, borrowing 1 degree as 60 minutes if necessary, similar to subtraction in time calculations.