Convert each angle measure to decimal degree form: -134 degrees 30 minutes
The Correct Answer and Explanation is:
To convert an angle in degrees and minutes to decimal degrees, we follow these steps:
1. Understanding the format
The angle given is in the format of degrees and minutes. In this case, we have:
- Degrees: -134°
- Minutes: 30′
In the conversion process, we need to convert minutes into a fraction of a degree.
2. Converting minutes to a decimal
There are 60 minutes in 1 degree. So, to convert minutes to decimal form, we divide the number of minutes by 60.30 minutes÷60=0.530 \text{ minutes} \div 60 = 0.530 minutes÷60=0.5
3. Adding the decimal value to the degrees
Now that we have the decimal equivalent of the minutes (0.5), we add it to the degrees value:−134+0.5=−133.5-134 + 0.5 = -133.5−134+0.5=−133.5
4. Result
Thus, the angle of -134 degrees 30 minutes in decimal degree form is -133.5 degrees.
Explanation
The conversion from minutes to decimal degrees is straightforward: divide the minutes by 60 to get the decimal part of the degree. In this case, 30 minutes is equivalent to 0.5 degrees, and adding this to -134 degrees gives the final result. It’s important to keep the negative sign since the angle is in the negative direction (which typically represents angles measured clockwise from the positive x-axis).
