How Many Angles Does a Regular Polygon Have

Firstly we will find interior angle. A polygon is a plane shape bounded by a finite chain of straight lines.

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Now we can use formula.

. How many lines of symmetry does a regular polygon with 20 sides have. If a regular polygon has an interior angle of 1755 how many sides does it have. Interior and exterior angles are supplementary thats their sum is 180.

Hence the number of sides a regular polygon has if its interior angle is 165 degrees are 24. Now we can solve for n. 360 15.

The sum of the exterior angles of any regular polygon is 360 degrees. The measure of exterior angle 24. The sum of the exterior angles of a regular polygon is 360 so if an exterior angle 8 then the number of sides is 3608 45.

The sum of all exterior angles is 360 degrees so there must be 36020 sides 18 sides. Allow s to represent the number of sides of the polygon. Hence the regular polygon has 24 sides.

Interior angle of a regular polygon of n sides nn2180 Exterior angle of a regular polygonof n sidesGiven nn2180 8 n360 n28 180 360 16n18. The measure of exterior angle 180 165 15 no. Of sides x measure of exterior angle 360 Solution.

Of sides 36015 24. Of sides x measure of exterior angle 360. The measure of interior angle 165 Find out.

Also we know that the sum of all exterior angles of any polygon is 360 degree. If the interior angle of a regular polygon is 160 degrees then the exterior angle is 20 degrees. Interior angle of a polygon sum of interior angles number of sides.

Thus the regular polygon has 15 sides. The formula for calculating the size of an interior angle is. Thus the regular polygon has 24 sides.

By the Exterior Angle Formula the sum of the exterior angles in any polygon is 360Since the polygon is regular all the angles are congruentThis is very important. Learn how to determine the number of sides of a regular polygon. Lets assume that the number of sides of the given regular polygon is n.

We have to find the number of sides of a polygon. Of sides x measure of exterior angle 360 no. 10 lines of symmetry connecting a pair of opposite vertices.

Therefore exterior angle 180-x 180 165 15. If the polygon was not regular the exterior angles could be 30 170 and 160. Therefore number of sides 360 each exterior angle.

N160 o180 0n2 n89n2 8n9n18. What is pentagon sides. Thus the regular polygon has 15 sides.

A pentagon is a geometrical shape which has five sides and five angles. We can plug value. As the polygon is a regular polygon each of its angle will be equal 160 o.

In both cases you must get the same result for what the interior angles add up to. This means sum of all its interior angles n160 o. The General Rule If it is a Regular Polygon all sides are equal all angles are equal Shape Sides Each Angle Triangle 3 60 Quadrilateral 4 90 Pentagon 5 108 How many sides does a.

We have to find the number of sides of a polygon. Exterior angle is 1 degree. How many sides does a regular polygon have if each interior angle is 90.

Then the number of interior angles the number of sides n. Measure of each exterior angle 24 Number of sides Sum of exterior angles each exterior angle 360 24 15. 2 From eqn 1 and 2 we get.

What is the interior angle of a 7 sided polygon. What is the measure of one of its exterior angles. Of sides 36024.

Interior angle 180 - 1. Interior angle 180 - exterior angle. Measure of each exterior angle 180 - 165 15 Since an interior and an exterior angle forms a linear pair Number of sides Sum of exterior angles Each exterior angle.

If a regular polygon has an interior bartleby. The exterior angles of a regular polygon are also equal. Total sum of all the exterior angles of the regular polygon 360 Let number of sides be n.

Anyway we can name the number of sides s and the number of angles aBecause every polygon has the. Interior angles of any polygon with n sides always add up to 180n-2 degrees. An equilateral triangle is a regular polygon with three equal side lengths and three equal angles.

NCERT Solutions for Class 8 Maths Chapter 3. 360 15. Now we can plug angle.

The polygon has 10 sides. 1 Expert Answer. If a polygon is a regular polygon with n sides and each interior angle is 179 degrees then its interior angles will add up to 179 n.

So The number of sides are 360. Interior angle 179. 20-gon has 20 lines of symmetry.

Answer A regular polygon with each interior angle measuring 165 has 24 sides.

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