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. Polygons can be regular or irregular. If the angles are all equal and all the sides are equal length it is a regular polygon. All the interior angles in a regular polygon are equal.

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.

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.

All the interior angles in a regular polygon are equal. The number of sides of the regular polygons where we are only shown one side. Kindergarten Worksheets.

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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. That's easy! By definition, all the interior angles of a square are right angles -- That means that they are all 90 degrees. To figure out the measure of the interior angles of a regular pentagon, hexagon, heptagon, etc, we need more than just a protractor! What if we needed to find the interior angle of a regular polygon with sides? That might be a little difficult to draw! Here are two methods to find the measure of the interior angles of a regular polygon:. For both methods, we will use the fact that the sum of the measures of the interior angles of a triangle is degrees!

How to find interior angle of regular polygon

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:.

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Find angle y which is within one of the interior angles. Maths Games. Our Journey. The number of sides of the regular polygons where we are only shown one side. Other lessons in this series include:. Close Privacy Overview This website uses cookies to improve your experience while you navigate through the website. Method 2. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. How many sides does the polygon have? The number of triangles a polygon can be split into is always 2 less than the number of sides. About Us.

A polygon has two types of angles - interior angles and exterior angles. The angle formed by any two adjacent sides with in the polygon is called its interior angle.

They are the angles within a polygon made by two sides:. Now, if we divide it by n, that is, 3, we get 60, which is the measure of an interior angle of a triangle. The formula for calculating the size of an interior angle is:. Find out more about our GCSE maths tuition programme. 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. More guides on this topic. Finding a single interior angle of a regular polygon Finding a single interior angle of an irregular polygon Finding the number of sides given the interior angle of a regular polygon Multiple shapes Problem solving to find the number of side Problem solving to find the number of angles. Types of angle Angles at a point and on a straight line Angles in parallel lines Triangles Quadrilaterals Polygons Symmetry. You also have the option to opt-out of these cookies. What are interior angles of polygons? The diagram below shows a regular decagon. Calculate the number of sides each regular polygon has.