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

Verified step by step guidance

1. First, separate the degrees and minutes for each angle: 55° 30', 12° 44', and 8° 15'.
2. Add the degrees and minutes of the first two angles: add 55° and 12° for degrees, and 30' and 44' for minutes.
3. If the sum of the minutes is 60 or more, convert 60 minutes into 1 degree and add it to the degrees sum, then subtract 60 from the minutes sum.
4. Next, subtract the third angle (8° 15') from the result obtained in the previous step by subtracting degrees and minutes separately.
5. If the minutes in the subtraction step are negative, borrow 1 degree (which equals 60 minutes) from the degrees part, add 60 to the minutes, and then perform the subtraction.

Key Concepts

Angle Measurement in Degrees and Minutes

Angles can be expressed in degrees (°) and minutes ('). One degree equals 60 minutes, similar to how time is measured. Understanding this notation is essential for performing accurate calculations involving angles.

Addition and Subtraction of Angles

When adding or subtracting angles, degrees and minutes must be handled separately. If the minutes exceed 60, convert the excess into degrees. Similarly, if subtracting results in negative minutes, borrow one degree to adjust the minutes.

Borrowing and Carrying in Angle Calculations

Borrowing and carrying are techniques used to manage minutes during addition or subtraction. For example, if minutes sum to more than 60, carry over the extra 60 minutes as one degree. If minutes are insufficient during subtraction, borrow one degree (60 minutes) to complete the operation.