How To Calculate The Sum Of Interior Angles 8 Steps For example, for a hexagon you should draw three lines, dividing the shape into 4 triangles. 4. multiply the number of triangles you created by 180. since there are 180 degrees in a triangle, by multiplying the number of triangles in your polygon by 180, you can find the sum of the interior angles of your polygon. [8]. 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.
Work Out The Sum Of Interior Angles The first method is to work out how many triangles we can divide the decagon into, and then multiply this by 180°. this gives 8 × 180 = 1440. the interior angles in a decagon sum to 1440°. the. We will call these angles x: we know that angles around a point add to 360°. therefore: 60 2x =360 2x =300 x =150 60 2 x = 360 2 x = 300 x = 150. this means that each interior angle of the regular polygon is 150°. so the sum of interior angles is equal to 150 × n or 150n: 150n = (n – 2) × 180. we can now solve for n:. Therefore, sum of the interior angles = (2 × 19 – 4) × 90°. = (38 – 4) 90°. = 34 × 90°. = 3060°. 2. each interior angle of a regular polygon is 135 degree then find the number of sides. solution: let the number of sides of a regular polygon = n. then the measure of each of its interior angle = [ (2n – 4) × 90°] n. The sum of interior angles can be obtained by dividing it into triangles. for example, the pentagon below has been divided into 3 triangles by joining the vertices 2 with 5 and 3 with 5. now the sum of the interior angles of the pentagon will be the sum of the interior angles of the three triangles, that is, \( 3\times 180^{\circ} = 540^{\circ} \).
Comments are closed.