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What is the sum of a convex polygons exterior angles?
Remember that the internal angle of a regular convex polygon is (n - 2) * 180 degrees / n, where n is the number of sides in the polygon. Also remember that the external angle of a regular convex polygon is 180 degrees minus the internal angle a polygon. So the external angle of a polygon is 180 - ((n - 2) * 180 / n). The sum of the angles will be the external angle multiplied by n, or: (180 - ((n - 2) * 180) / n ) * n = 180 * n - (n - 2) * 180 Please note that I only proved this for regular polygons, but this formula should also extend to irregular convex polygons too. If a teacher asks you for a proof, then this will be insufficient.
Why do All polygons have exterior angles that sum to 360 degrees?
Only convex man, if the angle is concave it would not be 360 degree.
What to regular polygons has a larger exterior angle?
An equilateral triangle is the only polygon in which the exterior angle is larger than the interior angle. They are equal in a square and smaller in all regular polygons with more sides,
Which of the polygons cannot be used to create a pure tessellation?
The only regular polygons which will tessellate are those with 3, 4 or 6 sides. But all irregular triangles, all irregular quadrilaterals, 15 classes of irregular convex pentagons and 3 classes of irregular convex hexagons will tessellate. In addition, there are concave polygons with different numbers of sides which will also tessellate.
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.
