To express the angle $58.45^\circ$ in degrees and minutes, follow these steps:

1. The integer part, $58$, is the number of degrees.
2. To find the number of minutes, multiply the decimal part $0.45$ by 60: $0.45 \times 60 = 27 \, \text{minutes}.$

Final Answer:

$58.45^\circ = 58^\circ 27'$

Let me know if you'd like further clarification! Here are some additional questions for exploration:

1. What are the steps for converting decimal degrees into degrees, minutes, and seconds?
2. How would $58.75^\circ$ convert to degrees and minutes?
3. How do you convert back from degrees and minutes to decimal degrees?
4. What is the smallest value of a decimal degree that corresponds to 1 minute?
5. How would this conversion apply in real-world contexts, such as navigation or geography?

Tip: Remember, 1 degree equals 60 minutes, so converting between them is straightforward with multiplication or division!