Show Another example: TrianglesThe Interior Angles of a Triangle add up to 180°
Let's try a triangle: 90° + 60° + 30° = 180° It works for this triangle
Now tilt a line by 10°:
80° + 70° + 30° = 180° It still works! Quadrilaterals (Squares, etc)(A Quadrilateral has 4 straight sides)
Let's try a square: 90° + 90° + 90° + 90° = 360° A Square adds up to 360°
Now tilt a line by 10°:
80° + 100° + 90° + 90° = 360° It still adds up to 360° The Interior Angles of a Quadrilateral add up to 360° Because there are 2 triangles in a square ...The interior angles in a triangle add up to 180° ... ... and for the square they add up to 360° ... ... because the square can be made from two triangles! A pentagon has 5 sides, and can be made from three triangles, so you know what ... ... its interior angles add up to 3 × 180° = 540° And when it is regular (all angles the same), then each angle is 540° / 5 = 108° (Exercise: make sure each triangle here adds up to 180°, and check that the pentagon's interior angles add up to 540°) The Interior Angles of a Pentagon add up to 540° The General RuleEach time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:
So the general rule is:
Sum of Interior Angles = (n−2) × 180° Each Angle (of a Regular Polygon) = (n−2) × 180° / n Perhaps an example will help:
Sum of Interior Angles = (n−2) × 180° = (10−2) × 180° = 8 × 180° = 1440° And for a Regular Decagon: Each interior angle = 1440°/10 = 144°
Note: Interior Angles are sometimes called "Internal Angles" Copyright © 2020 MathsIsFun.com
Interior angle formulas are used to find interior angles associated with a polygon and their sum. Interior angles are the angles that lie inside a shape, generally a polygon. Also, the angles lying in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles. Let us understand the interior angle formula in detail in the following section.
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Let us consider a polygon of n sides. Then by interior angle formula to find the sum of interior angles of a polygon is given as, The sum of interior angles = 180(n-2)ºThe interior angles of a polygon always lie inside the polygon and the formula to calculate it can be obtained in three ways. Formula 1: For “n” is the number of sides of a polygon, formula is as, Interior angles of a Regular Polygon = [180°(n) – 360°] / nFormula 2: The formula to find the interior angle, if the exterior angle of a polygon is given, Interior Angle of a polygon = 180° – Exterior angle of a polygonFormula 3: If the sum of all the interior angles of a regular polygon, the measure of interior angle can be calculates using the formula,
Interior Angle = Sum of the interior angles of a polygon / n where,“n” is the number of polygon sides Let us understand interior angle formulas better using solved examples.
Solved Examples Using Interior Angle Formula
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