Complete the table: Convex polygon Number of sides Number of triangles Sum of interior angles Triangle

Given, convex polygon is triangle. Therefore, number of sides = 3 So, number of triangles formed by the diagonal = n - 2 = 3 - 2 = 1 Now, sum of the interior angles of the polygon = 2 n - 4 × 90 ° = 2 × 3 - 4 × 90 ° = 6 - 4 × 90 ° = 2 × 90 ° = 180 ° Convex polygon Number of sides Number of triangles Sum of interior angles Triangle 3 1 180 °

Complete the table: Convex polygon Number of sides Number of triangles Sum of interior angles Quadrilateral 4

Given, convex polygon is quadrilateral. Thus, number of sides = 4 So, number of triangles formed by the diagonals = n - 2 = 4 - 2 = 2 Now, sum of the interior angles of the polygon = ( 2 n - 4 ) × 90 ° = 2 × 4 - 4 × 90 ° = 8 - 4 × 90 ° = 4 × 90 ° = 360 ° Convex polygon Number of sides Number of triangles Sum of interior angles Quadrilateral 4 2 360 °

Complete the table: Convex polygon Number of sides Number of triangles Sum of interior angles Pentagon

Given, convex polygon is pentagon. Therefore, number of sides = 5 So, number of triangles formed by the diagonal = n - 2 = 5 - 2 = 3 Now, sum of the interior angles of the polygon = ( 2 n - 4 ) × 90 ° = 2 × 5 - 4 × 90 ° = 10 - 4 × 90 ° = 6 × 90 ° = 540 ° Convex polygon Number of sides Number of triangles Sum of interior angles Pentagon 5 3 540 °

Copy and complete the table Convex polygon Number of sides Number of triangles Sum of interior angles 4

Given, number of triangles formed by the diagonal of the convex polygon are 4 . We know that, number of triangles formed by the diagonal of the convex polygon = n - 2 . ⇒ 4 = n - 2 ⇒ n - 2 = 4 ⇒ n - 2 + 2 = 4 + 2 [By transposition] ⇒ n = 6 Hence, number of sides are 6 and the convex polygon is hexagon. Now, Sum of the interior angles of a hexagon = ( 2 n - 4 ) 90 ° . = ( 2 × 6 - 4 ) 90 ° = ( 12 - 4 ) 90 ° = 8 × 90 ° = 720 ° Therefore, sum of the interior angles of the hexagon = 720 ° Convex polygon Number of sides Number of triangles Sum of interior angles Hexagon 6 4 720 °

Copy and complete the table Convex polygon Number of sides Number of triangles Sum of interior angles 7

Given, number of sides of the convex polygon are 7 . Therefore, the convex polygon is heptagon We know that, number of triangles formed by the diagonal of the convex polygon = n - 2 . = 7 - 2 = 5 Hence, number of triangles formed by the diagonals of the heptagon are 5 . Now, Sum of the interior angles of a hexagon = ( 2 n - 4 ) 90 ° . = ( 2 × 7 - 4 ) 90 ° = ( 14 - 4 ) 90 ° = 10 × 90 ° = 900 ° Therefore, sum of the interior angles of the hexagon = 900 ° Convex polygon Number of sides Number of triangles Sum of interior angles Heptagon 7 5 900 °

Copy and complete the table Convex polygon Number of sides Number of triangles Sum of interior angles 6

Given, number of triangles formed by the diagonal of the convex polygon are 6 . We know that, number of triangles formed by the diagonal of the convex polygon = n - 2 . ⇒ 6 = n - 2 ⇒ n - 2 = 6 ⇒ n - 2 + 2 = 6 + 2 [By transposition] ⇒ n = 8 Hence, number of sides are 8 and the convex polygon is octagon. Now, Sum of the interior angles of a hexagon = ( 2 n - 4 ) 90 ° . = ( 2 × 8 - 4 ) 90 ° = ( 16 - 4 ) 90 ° = 12 × 90 ° = 1080 ° Therefore, sum of the interior angles of the hexagon = 720 ° Convex polygon Number of sides Number of triangles Sum of interior angles Octagon 8 6 1080 °

Copy and complete the table Convex polygon Number of sides Number of triangles Sum of interior angles Nonagon

Given, convex polygon is Nonagon. Therefore, number of sides = 9 . So, number of triangles formed by the diagonal is n - 2 . = 9 - 2 = 7 Now, sum of the interior angles of the polygon = ( 2 n - 4 ) 90 ° . = ( 2 × 9 - 4 ) 90 ° = ( 18 - 4 ) 90 ° = 14 × 90 ° = 1260 ° Convex polygon Number of sides Number of triangles Sum of interior angles Triangle 9 7 1260 °

Copy and complete the table Convex polygon Number of sides Number of triangles Sum of interior angles Decagon

Given, convex polygon is Decagon. Therefore, number of sides = 10 . So, number of triangles formed by the diagonal is n - 2 . = 10 - 2 = 8 Now, sum of the interior angles of the polygon = ( 2 n - 4 ) 90 ° . = ( 2 × 10 - 4 ) 90 ° = ( 20 - 4 ) 90 ° = 16 × 90 ° = 1440 ° Convex polygon Number of sides Number of triangles Sum of interior angles Decagon 10 8 1440 °