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The sum of the exterior angles of a polygon is 360o, so for a regular n-sided polygon, each is 360o/n.
The interior and exterior angles of a polygon are supplementary, that is sum to 180o.
For a regular 15 sided polygon:
exterior_angle = 360o / 15
= 24o
interior_angle = 180o - exterior_angle
= 180o - 24o
= 156o
Alternatively:
The sum of the interior angles of a n-sided polygon is (n-2) x 180o, so for a regular n-sided polygon each interior angle is (n-2) x 180o / n.
For a 15 sided polygon:
interior_angle = (15 - 2) x 180o / 15
= 13 x 12o
= 156o
exterior_angle = 180o - interior_angle
= 180o - 156o
= 24o.
What else can I help you with?
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.
How many sides does a regular polygon have if its exterior angles are equal to its interior angles?
4 such as a square
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.
What is the measure of an interior angle for a regular ten-sided polygon?
144o. Sum of exterior angles of a polygon is 360o. Each exterior angle for a regular decagon is 360o / 10 = 36o. Exterior and interior angles are supplementary, that is sum to 180o. Therefore the interior angle of a regular decagon is 180o - 36o = 144o.
What size are exterior angles on a regular polygon have if each interior angle is 172.5 and how many sides does it have?
Exterior angles are 7.5 There are 48 sides.
If the sum of the interior angles of a polygon equals the sum of the exterior angles what is the name of the polygon?
A Regular Polygon
Which regular polygon's interior angles is three times that of its exterior angles?
octagon interior=135 exterior=45
Which regular polygon's interior angles are half that of its exterior angles?
An equilateral triangle.
What type of regular polygon has equal interior and exterior angles?
A quadrilateral.
A regular polygon with interior and exterior angles that equal?
Square or rectangle
What is the sum of the measures of the interior angles of the regular polygon if each exterior measures 120?
Hint: in a regular polygon interior plus exterior = 180o, always.
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.
How many sides of a regular polygon with interior angles of 178?
Interior angles 178 so exterior angles 2. Number of sides of any regular polygon = 360/exterior angle You polygon has 180 sides. Bet you're glad you didn't have to sketch it!
A regular polygon an exterior angle of 30 What is the size of the interior angle?
Exterior angles are supplementary with interior angles, so 180-30=150
How many sides does a regular polygon have if its exterior angles are equal to its interior angles?
4 such as a square
What is the sum of the measures of the interior angles of a regular of a regular polygon if each exterior angle measures 120?
If exterior angles are 120 then interior angles must be 60 so you have an equilateral triangle
What are the interior and exterior angles of a regular polygon?
If the polygon has n sides, each exterior angle is 360/n degrees.The interior angle is 180 less exterior angle.
