Perform each calculation. See Example 3. 55° 30' + 12° 44' ― 8° 15'

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Convert each angle from degrees and minutes to just minutes. For example, 55° 30' becomes (55 * 60) + 30 minutes.

Perform the addition of the angles in minutes: add the minutes from 55° 30' and 12° 44'.

Subtract the minutes from 8° 15' from the result obtained in the previous step.

Convert the final result back to degrees and minutes by dividing the total minutes by 60 to get degrees and using the remainder as minutes.

Ensure the final angle is expressed in the format of degrees and minutes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angle Addition and Subtraction

In trigonometry, angles can be added or subtracted to find a resultant angle. This is particularly important when dealing with angles expressed in degrees and minutes, as seen in the question. The process involves converting all angles to a common format, performing the arithmetic, and then converting back if necessary.

Degrees and Minutes

Angles can be measured in degrees, where one degree is divided into 60 minutes. This notation is crucial for precise calculations in trigonometry, especially when dealing with non-integer angles. Understanding how to convert between degrees and minutes is essential for performing operations like addition and subtraction accurately.

Conversion of Angles

When performing calculations with angles, it may be necessary to convert between different formats, such as degrees to radians or degrees and minutes to decimal degrees. This conversion is vital for ensuring that all angles are in the same format before performing arithmetic operations, which helps avoid errors in calculations.

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