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Calculate the number of sides of a regular polygon whose interior angles are each 156 degrees?
Exterior angle = 180-156 = 24 degrees
Number of sides = 360/24 = 15 sides.
If you can't remember the formula, then remember this to help figure it out:
The regular polygon can be divided into triangles (like Pizza slices). Each triangle is an isosceles triangle and all of them are congruent (since it's a regular polygon).
Take one of the triangles: each of the 'leg angles' will be half of the polygon angle (the leg of the triangle has bisected the polygon angle). So these two angles will add together to be the same measure as the polygon angle (call it Ap). So the other angle in the triangle is in the center and all these pizza slice angle make a circle in the middle (360°). Since the triangle sums to 180°, the angle in the middle is (180° - Ap), then you have:
Number of sides = (360°) / (180° - Ap), or in this case: 360/(180-156) = 15 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
How many sides does a regular polygon if its interior angles are 270?
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.
Calculate the number of sides of a regular polygon whose interior angles are each 165 degrees?
14 sides in the polygon
How many sides does a regular polygon have with an interior of 178 degrees?
It has 180 sides if the interior of the (regular) polygon has a total of 178 'degrees'.
How many sides does a regular polygon have if its interior angles are all 15 degrees?
The interior angles of a regular polygon must be 60 degrees or greater.
If the measure of one interior angle of a regular polygon is 90 degrees how many sides does the polygon have?
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.
An interior angle of a regular polygon is found to be 108 degrees What is the regular polygon called?
Obtuse
What measure of the interior angles of a polygon is 720 degrees?
If it's a regular polygon then each interior angle measures 120 degrees.
How many sides does a 24 degrees polygon have?
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.
What is the Interior angle of a polygon with 15 sides?
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.
Which regular polygon has interior angles that measure about 152.3 degrees each?
A 13 sided regular polygon
The sum of the interior angles of a 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.
Calculate the measure of a central angle of a regular ten-sided polygon.?
Each interior angle of a regular 10 sided decagon measures 144 degrees
