Vertical angles are not a specific angle. It is the term used to describe two angles with a common vertex and are usually made up of the same lines. They are always congruent.
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A regular pentagon has 5 sides and each interior angle measures 108 degrees not 172 degrees
ummm a square ☺ ummm a square ☺
I think you mean 108 degrees (superscript "o" is often used for "degrees"). From another answer in this section, using s=number of sides=Number of angles, you get angle = 180(1 - 2/s) which can be turned around to 2/s = 1 - angle/180 or s=360/(180-angle) So for 108 degrees you get s=360/(180-108) which is 360/72 = 5 sides.
360.
360