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Why must a regular polygon's interior angles have a measure that is a divisor a 360?
Wiki User
∙ 13y ago
The statement is not correct.
The sum of the interior angles of an n-sided polygon is (n-2)*180 degrees.
If n is odd, the sum will not be a divisor of 360.
And each individual interior angle will be 180*(n-2)/n degrees. And that will be a divisor of 360 only if n = 3 (triangle), 4 (square) or 6 (hexagon).
And, not by coincidence, these are the only regular polygons that will tessellate a plane surface.
Wiki User
∙ 13y ago
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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.
What are regular polygons?
Regular polygons are those polygons that are bothequilateral (all sides congruent) and equilateral (all interior angles congruent).
Which regular polygons has the larger interior angle pentagon or square?
pentagon
What name is given to polygons whose angles all have the same measure?
regular polygons
Are all polygons are equilateral?
Yes in general polygons that have equal interior angles also have equal sides and they are said to be regular polygons. But a rectangle is an exception.
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.
What is the measure of an interior angle of a regular polygon with 6 sides?
120See related link below for interior angles of various polygons.
What are regular polygons?
Regular polygons are those polygons that are bothequilateral (all sides congruent) and equilateral (all interior angles congruent).
Which regular polygons has the larger interior angle pentagon or square?
pentagon
What name is given to polygons whose angles all have the same measure?
regular polygons
Are all polygons are equilateral?
Yes in general polygons that have equal interior angles also have equal sides and they are said to be regular polygons. But a rectangle is an exception.
Is a concave polygon is regular?
By definition a regular polygon cannot be concave. Concave polygons contain one or more interior angles that are greater than 180 degrees, and regular polygons can never have an interior degree greater than 180 degrees.
Which of these two regular polygons has the larger interior angle a triangle or hexagon?
Hexagon.
What shape has 45 degree interior angles?
There is no such regular polygon with 45 degree interior angles; the smallest interior angles in regular polygons are 60 degrees, which is found in a triangle.
Which of these two regular polygons has the larger interior square or pentagon?
Each interior angle of a square is 90 degrees Each interior angle of a regular pentagon is 108 degrees
What do you call polygons in which all sides have the same length and all angels have the same measure?
regular polygons
What is the measure of each exterior angle of a regular 2x-gon?
Regular Polygons
