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In a tessellation a number of polygons meet at a point. If n polygons meet, then there will be n vertices. These must add up to 360 degrees so that the tessellation does not leave holes. So the interior angles of the polygon must be a factor of 360 degrees.
Interior angle of an equilateral triangle = 60 deg = 360/6 and so it will tessellate;
Interior angle of a square = 90 deg = 360/4 and so it will tessellate;
Interior angle of a regular pentagon = 108 deg which is not a factor of 360 and so it will not tessellate;
etc.
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What regular polygons have rotational symmetry?
All of them have rotational symmetry because all the sides and angles have to be the same in order for the polygon to be a regular polygon
What shape has a rotational symmetry of 120 degree?
An equilateral triangle, and all regular polygons with 3n sides.
How do you work out the sum of exterior angles for a pentagon?
all regular polygons (such as a pentagon) have the sum of their exterior angles = 360 degrees
What is the measure of an exterior angle of a regular polygon with 8 sides?
All polygons exterior angles sum to 360. If it is regular it means all angles are equal So all 8 angles are the same number 8x = 360 x = 45 Each angle is 45 degrees
Is a pentagon a regular polygon sometimes always or never?
All polygons can be irregular sense the requirements for a polygon to be irregular is for 1 or more sides to be unequal to the others. So a pentagon is sometimes a regular polygon. Hope that answers your question.
