Q16 of 805 Page 17

i. Each interior angles of a regular octagon is

ii. The sum of all interior angle of a regular hexagon is


iii. Each exterior angle of a regular polygon is 60°. This polygon is a ...... .


iv. Each interior angle of a regular polygon is 108°. This polygon is a ...... .


v. A pentagon has ...... diagonals.


(i) Octagon has 8 sides


Each interior angle = 180° - 360°/n


=180° - 360°/8


=180° - 45° = 135°


(ii) Hexagon has 6 sides


Sum of all interior angle = (n -2) × 180°


=(6 - 2) × 180°


=(4) × 180° = 720°


(iii) For n sided polygon.


Exterior angle =


Therefore , = 60


→ n = 6


The regular polygon has 6 sides. it is a regular hexagon


(iv) For n sided polygon.


Interior angle =


Therefore , = 108


→


→ n = 5


The regular polygon has 5 sides. it is a regular pentagon


(v) Number of diagonals in n sided polygon =


Therefore , n = 5


Diagonals = = 5


More from this chapter

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14

For a convex polygon of n sides, we have:

i. Sum of all exterior angles = ...... .


ii. Sum of all interior angles = ...... .


iii. Number of diagonals = ...... .


 15

For a regular polygon of n sides, we have:

i. Sum of all exterior angles = ...... .


ii. Sum of all interior angles = ...... .


 17

Write ‘T’ for true and ‘F’ for false of each of the following:

i. The diagonals of a parallelogram are equal.


ii. The diagonals of a rectangle are perpendicular to each other.


iii. The diagonals of a rhombus bisect each other at right angles.


iv. Every rhombus is a kite.


 18

Construct a quadrilateral PQRS in which cm, cm and cm.