Angles in Polygons
Angles in Polygons
Identifying Polygons
- Polygons are figures that are made up of straight lines that form a closed shape.
- There are several types of polygons, including triangles, quadrilaterals, pentagons, hexagons, etc., named according to the number of sides.
- Polygons have interior and exterior angles.
Angle Properties of a Triangle
- A triangle is a polygon with three sides.
- The sum of the interior angles in a triangle is 180 degrees.
Angle Properties of Quadrilaterals
- A quadrilateral is a polygon with four sides.
- The sum of the interior angles in a quadrilateral is 360 degrees.
Angle Properties of Other Polygons
- For polygons with more than four sides, the sum of the interior angles can be found using the formula (n-2) x 180 degrees, where ‘n’ is the number of sides of the polygon.
- For example, a pentagon has five sides, so its interior angles sum up to (5-2) x 180 = 540 degrees.
Finding an Individual Angle in Regular Polygons
- A polygon is regular if all its sides and angles are equal.
- To find each interior angle of a regular polygon, divide the total sum of the interior angles by the number of sides.
- For example, each interior angle of a regular hexagon (6 sides) is (6-2) x 180 / 6 = 120 degrees.
Exterior Angles of Polygons
- The exterior angle of a polygon is formed by extending one of its sides.
- The sum of the exterior angles for any polygon will always be 360 degrees.
- For a regular polygon, each exterior angle is 360 degrees / n, where ‘n’ is the number of sides of the polygon.