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Each interior angle if a regular polygon measurses 172 degrees how many sides does the polygon have?
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.
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Can a regular polygon's interior angles measure 40 degrees?
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.
What is the interior angle measure if a 16 sided polygon?
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
If a regular polygon has interior angles that measure 720 degrees how many sides does the polygon have?
6
If the exterior angle of a regular polygon is 108 degrees how many sides does the polygon have?
That's true if the interior angles are 108 degrees, but a regular polygon cannot have exterior angles of 108 degrees.
Interior angle of 7 sided polygon?
Providing that it is a regular 7 sided polygon then each interior angle is 900/7 degrees
