Understanding Angular Measurement: Degrees to Minutes

Angular measurement is a way to quantify angles. The most common unit is the degree ($^\circ$). A full circle is divided into 360 degrees.

The Degree-Minute-Second System

Just like time is measured in hours, minutes, and seconds, angles can also be broken down into smaller units:

• Minutes of arc ($'$): Each degree is divided into 60 smaller units called minutes.
• Seconds of arc ($''$): Each minute is further divided into 60 seconds.

This system helps in precisely measuring angles, especially in fields like astronomy and navigation.

Conversion Factors

The fundamental relationship between degrees and minutes is:

$$1^\circ = 60'$$

Similarly, the relationship between minutes and seconds is:

$$1' = 60''$$

To convert degrees directly to seconds, you multiply by both factors:

$$1^\circ = 1^\circ \times \frac{60'}{1^\circ} \times \frac{60''}{1'} = 3600''$$

Analyzing the Options

Let's look at the provided options in light of these definitions:

Therefore, one degree is equivalent to 60 minutes of arc.