1. Are there any other units for measuring angles besides degrees and minutes?
The other system is called radians. You can change the mode of your calculator to operate using radians (RAD) instead of degrees (DEG). Remember to change it back!
2. Why are there 360 degrees in a one revolution?
The Zodiac was first divided into 360. The Greek astronomer Hipparchus first divided a circle into 360 degrees. 360 is also approximately the number of days in a year.
3. Are vertically opposite angles always equal?
Providing the two intersecting lines are both straight lines.
4. Are congruent angles and equal angles the same thing?
A pair of congruent angles are the same size and a pair of equal angles are the same size.