The easiest way to solve this is to use the exterior angles of the polygon.
The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o.
As the polygon is regular, all the interior angles are the same and all the exterior angles are the same.
So, for an interior angle of 172o the exterior angle is 180-172 = 8o.
The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45.
Thus the polygon with interior angles of 172o has 45 sides.
No. To elaborate, the smallest regular polygon, an equilateral triangle, has 60 degree interior angles. The next larger one, a square, has 90 degree interior angles. In fact, for any regular polygon, the interior angles measure 180*(n-2)/n degrees, where n is the number of sides. No polygon has less than 3 sides. Thus, no regular polygon can have interior angles less than 60 degrees.
The interior angles of a 16 sided polygon add up to 2520 degrees If it's a regular polygon then each interior angle measures 157.5 degrees
6
That's true if the interior angles are 108 degrees, but a regular polygon cannot have exterior angles of 108 degrees.
Providing that it is a regular 7 sided polygon then each interior angle is 900/7 degrees
No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more.
It has 180 sides if the interior of the (regular) polygon has a total of 178 'degrees'.
The interior angles of a regular polygon must be 60 degrees or greater.
The only regular polygon with an interior angle of 90 degrees is the square, which has four sides. Other polygons can have an interior angle of 90 degrees, but they would not be regular polygons.
Obtuse
If it's a regular polygon then each interior angle measures 120 degrees.
It cannot be a regular polygon with interior angles of 24 degrees since the smallest interior angle in a regular polygon is 60 degrees. If it is an irregular polygon, then any one of them, with 3 or more sides, can have an angle of 24 degrees.
The interior angles of a 15 sided polygon add up to 2340 degrees and if it is a regular polygon then each interior angle is 156 degrees.
A 13 sided regular polygon
The sum of the interior angles of a n-sided polygon is (n-2)*180 degrees. This is true whether or not the polygon is regular.
It is 60 degrees.
No.