Question

Q.8.Find the following:
1)The measure of each angle of a regular Octagon will be how much.
2)No. of diagonals of a hectagon.
3)The no. Of a sides of a polygon which has 27 diagonals. ​

Answer 1

1) All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the angles, we know that the sum of all the angles is 1080 degrees (from above)... And there are eight angles... So, the measure of the interior angle of a regular octagon is 135 degrees.

2)A hexagon has 9 diagonals: there are three diagonals for every three vertices. A heptagon has 14 diagonals. Past the heptagon, it gets more difficult to count the diagonals because there are so many of them.

3)The formula for the no. of diagonals of a ’n' sided polygon is n(n-3)/2 .

It works for triangle (0 diagonals) , quadrilateral (2 diagonals) , pentagon (5 diagonals) and for every another polygon.

Let's come to the problem.

No. Of diagonals = n(n-3)/2 = 27

n(n-3) = 54

n^2 - 3n -54 = 0

n^2 - 9n + 6n - 54 = 0

n(n-9) + 6(n-9) = 0

(n-9)(n+6) = 0

n = 9, -6

(excluding -6)

n = 9

The polygon has 9 sides.