Converting Angle from Degrees and Minutes to Decimal Degrees

This question requires converting an angle measurement from the Degrees Minutes Seconds (DMS) format into decimal degrees.

Understanding Angle Units

• An angle can be measured in degrees (°).
• Degrees are further divided into minutes (‘).
• There are 60 minutes in 1 degree: $1^\circ = 60'$
• Minutes are further divided into seconds (“).
• There are 60 seconds in 1 minute: $1' = 60''$

Conversion Process

To convert an angle from degrees and minutes to decimal degrees, we need to convert the minutes part into degrees and add it to the degrees part.

The given angle is 60° 45’.

1. Identify the parts: The angle has 60 degrees and 45 minutes.
2. Convert minutes to degrees: Since $1' = \frac{1}{60}^\circ$, we can convert 45 minutes to degrees by dividing 45 by 60. $$ 45' = \frac{45}{60}^\circ $$
3. Simplify the fraction: $$ \frac{45}{60} = \frac{3 \times 15}{4 \times 15} = \frac{3}{4} $$
4. Convert the fraction to a decimal: $$ \frac{3}{4} = 0.75 $$ So, 45 minutes is equal to 0.75 degrees.
5. Add the decimal degrees to the degree part: $$ 60^\circ 45' = 60^\circ + 45' $$ $$ 60^\circ 45' = 60^\circ + 0.75^\circ $$ $$ 60^\circ 45' = 60.75^\circ $$

Conclusion

The angle 60° 45’ is equivalent to 60.75° in decimal degrees. This matches the first option.