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How many sides does a regular polygon have if the measures of each exterior angle equals 12 degrees?
The regular polygon whose exterior angle measure is 12 degrees, has 30 sides (360/12, since the exterior angles on any polygon always add up to 360 degrees).
In a regular polygon the ratio of the measure of the exterior angle to the measure of the adjacent interior angle is 4 to 1 how many sides does the polygon have Please show your work?
This is not possible for a normal regular polygon. (A regular polygon has all equal angles and all equal sides. A normal polygon has no intersecting edges.)The smallest regular polygon is an equilateral triangle (a three sided polygon), whose exterior angle measure is twice the measure of its interior angle. A four-sided polygon (a square) has equal interior and exterior angle measures of 90⁰. Starting from a five-sided polygon, the exterior angle measure is smaller than the interior angle measure.Let's assume that the given information is true. So we need to verify it.Let's say that the interior angle of the regular polygon has a measure of x degrees, and the measure of the exterior angle of that polygon is 4x degrees.Since the sum of the interior and the exterior angles of the polygon is 180 degrees (a straight line), the interior angle is 36 degrees.4x + x = 1805x = 1805x/5 = 180/5x = 36The sum of the angles of a polygon = 180⁰(n - 2), where n is the number of the sides of the polygon.The measure of one of the angles of a polygon = 180⁰(n - 2)/n. Substituting the angle measure of 36⁰ into this formula, we have:36⁰ = 180⁰(n - 2)/n (multiply by n to both sides)36⁰n = 180⁰(n - 2)36⁰n = 180⁰n - 360⁰ (add 360⁰ and subtract 36⁰n to both sides)360⁰ = 144⁰n (divide by 144⁰ to both sides)2.5 = n !!That means that a such normal polygon does not exist.
How many sides has a regular polygon whose interior angle is 11 times its exterior angles?
The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nThe measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nIf the interior angle is 11 times the exterior angle, then:180 (n-2)/n = 11 x 360/nthen: 180 n - 360 = 11 x 360, or180 n = 12 x 360that its solution gives n = 24Accordingly, the answer is that the number of sides of this polygon is 24
What is the name for two angles whose measures have the sum of 90 degrees?
The angles are complementary.
What is the sum of the interior angles of a polygon is 900 What type of polygon is it?
For any regular polygon with number of sides n, the sum of the internal angles is equal to (n - 2) x 180. Therefore, the number of sides of a shape the sum of whose internal angles are equal to 900 is equal to (n - 2) x 180 = 900, therefore, n = (900 / 180) + 2 = 7. The number of sides the shape will have is 7, making it a heptagon (also known as a septagon). It is not necessarily regular however, because although the angles in a regular heptagon would add to 900 degrees, an irregular heptagon would also add to this number.
