How to find interior angle of regular polygon

A polygon close polygon A polygon is a 2-dimensional closed shape with straight sides, eg triangle, hexagon, etc.

Here we will learn about interior angles in polygons including how to calculate the sum of interior angles for a polygon, single interior angles and use this knowledge to solve problems. Interior angles are the angles inside a shape. They are the angles within a polygon made by two sides:. The number of triangles a polygon can be split into is always 2 less than the number of sides. Step by step guide: Angles in polygons. Includes reasoning and applied questions. Interior angles of a polygon is part of our series of lessons to support revision on angles in polygons.

How to find interior angle of regular polygon

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. They can have any number of sides. Regular polygons have sides and angles of the same length. Many of the polygons like triangles, squares, and rectangles are used extensively for various purposes. To find the measure of one interior angle , we divide the result by n. For example, let's consider a 3-sided regular polygon, that is, an equilateral triangle. We use the formula, and substitute n with 3. Now, if we divide it by n, that is, 3, we get 60, which is the measure of an interior angle of a triangle. Note: The particular formula is true for only regular polygons, that is, where all the angles are the same, and does NOT cover other cases. About Us. Already booked a tutor?

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All angles are classified based on whether they are found inside or outside of any geometric shape into interior and exterior angles. Angles that are found inside or within any geometric shape are called interior angles. They are also sometimes called internal angles. A triangle has three interior angles. Similarly a quadrilateral such as a square, rectangle, parallelogram, kite, or a trapezoid has four interior angles. Again polygons such as pentagon, hexagon, heptagon, octagon, nonagon, and decagon have five, six, seven, eight, nine, and ten interior angles. To obtain the sum of interior angles we simply add the measures of all the angles found within the shape. To make the process less tedious, the sum of interior angles in all regular polygons is calculated using the formula given below:. To find the measure of a single interior angle of a regular polygon, we simply divide the sum of the interior angles value with the total number of sides. For an irregular polygon, the unknown angle can be determined when measure of all other angles and their sum are known.

How to find interior angle of regular polygon

With this polygon calculator, you can find the essential properties of any n-sided regular polygon. Whether you are looking for the area of a heptagon or the angles in a decagon, you're at the right place. Below, you'll find the polygon definition and a table with the names of polygons along with their shapes. After reading this short article, you'll know what a polygon is and how many sides a particular polygon has — keep reading, or simply give this calculator a go! A polygon is a 2D closed figure made up of straight line segments. That's the polygon definition. But what does it look like? Many shapes you learned about are polygons - triangles, squares, parallelograms, rhombus, kites, pentagons, hexagons, octagons A lot of them. But popular shapes that are not polygons also exist - take a circle and an ellipsis as an example.

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Includes reasoning and applied questions. We get the result to be How to find the measure of an interior angle of a regular polygon? Terms and Conditions. Learning checklist You have now learned how to: Use conventional terms for geometry e. Note that we know the values of all the other angles. Find the size of the other angle. This means the size of one interior angle. Related links. How many sides does the polygon have? Maths: Exam-style questions Personalise your Bitesize! Note whether this are regular or irregular shapes. Common misconceptions.

The sum of the measures of the interior angles of a triangle is degrees. Since all the sides of equilateral triangles are the same length, all the angles are the same The interior angles of an equilateral triangle are all 60 degrees.

Example 2: finding a single interior angle of an irregular polygon The diagram shows a polygon. The number of triangles in each polygon is two less than the number of sides. Identify what the question is asking you to find. Necessary Necessary. Unknown number of sides — regular shape. The number of triangles a polygon can be split into is always 2 less than the number of sides. Terms and Conditions. A polygon close polygon A polygon is a 2-dimensional closed shape with straight sides, eg triangle, hexagon, etc. Maths: Exam-style questions Personalise your Bitesize! Practice interior angles of a polygon questions. For example, let's consider a 3-sided regular polygon, that is, an equilateral triangle.