Regular Polygons With Interior Angles Studying Math Mathematics Education Math Formulas If it is a regular polygon (all sides are equal, all angles are equal) shape sides sum of interior angles shape each angle; triangle: 3: 180° 60° quadrilateral: 4: 360° 90° pentagon: 5: 540° 108° hexagon: 6: 720° 120° heptagon (or septagon) 7: 900° 128.57 ° octagon: 8: 1080° 135° nonagon: 9: 1260° 140° any polygon: n (n−2. We can learn a lot about regular polygons by breaking them into triangles like this: notice that: the "base" of the triangle is one side of the polygon. the "height" of the triangle is the "apothem" of the polygon. now, the area of a triangle is half of the base times height, so: area of one triangle = base × height 2 = side × apothem 2.
Interior Angles Of Regular Polygons In 2021 Basic Math Skills Study Regular polygons. secondary 1 2. polygons are often classified in reference to the measurements of their sides, angles, and diagonals. in some cases, the side and angle measurements of a polygon will be identical. the apothem. decomposition into triangles. the central angle. the angles of isosceles triangles. Sum of interior angles of a regular polygon. let there be a n sided regular polygon. since, the sides of a regular polygon are equal, the sum of interior angles of a regular polygon = (n − 2) × 180° for example, the sides of a regular polygon are 6. so, the sum of interior angles of a 6 sided polygon = (n − 2) × 180° = (6 − 2) × 180. Theorem 7.1.1 7.1. 1. the angle bisectors of each angle of a regular polygon meet at the same point. this point is called the center of the regular polygon. in figure 7.1.2 7.1. 2. o o is the center of each regular polygon. the segment of each angle bisector from the center to the vertex is called a radius. A start by noticing that each of the labeled angles is an corresponding to the pentagon in the middle of the logo. the sum of the measures of all the exterior angles of a polygon is 360^ (∘), according to the polygon exterior angles theorem. x 68^ (∘) 68^ (∘) 70^ (∘) 70^ (∘) = 360^ (∘) solve the equation for x.
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