if a polygon is regular, what's true about it's angles????

Question

i need a formula to show how to answer that

Answer 1

1. All angles are equal
2. All angles are less than 180°
3. Size of each angle = (180 - 360/n)° where n = number of sides

Answer 2

yeah, i just learned about this today and the packet is right here! here ya go:

all sides and angles are congruent (the same)

S (sum of all angles) = 180(n-2)

so, if you needed to find the sum of all the angles in, say, a pentagon (5 sides) you would do this:

S=180(n-2)
S=180(5-2)
S=180(3)
S=540

if you wanted to find how much each angle was, just divide that by 5 (108)

if you had the sum, but wanted to find out how many sides there were this is what you'd do..(ill just use a pentagon again)

S=180(n-2)
540=180(n-2)
540=180n-360
+360=180n
900=180n
900/180=180n/180
5=n

told ya! now that's just interior angles..

if you want exterior angles, remember this: THE EXTERIOR ANGLES ALWAYS EQUAL 360 degrees!!

if you wanted to find out what each one ws (pentagon, again), just do this:

360/5
72 -- each exterior angle is 72 degrees

if you wanted to find out how many sides there are, do this:

360/72
5 -- there are 5 sides


hope this helped and let you understande better! :-)

Answer 3

All the sides are the same length, all the interior angles are equal, and the exterior angles equal 360 degrees divided by the number of sides.

Answer 4

The definition of a regular polygon included that it must be 'equi-angular' which means that all the angles have the same measure. This is by definition.

If you are supposed to prove that something is regular, you have to prove that all it's sides are the same length, that all it's angles are the same measure, and that not of it's sides intersect one another.

Answer 5

all its angles are equal, as are its sides.