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Question

Fill in the blanks.
(i) Each interior angle of a regular octagon is (.........)°.
(ii) The sum of all interior angles 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.


Solution

(i) Octagon has 8 sides.
 Interior angle =180°n-360°nInterior angle =(180°×8)-360°8                       =135°
(ii) Sum of the interior angles of a regular hexagon = (6-2)×180=720

(iii) Each exterior angle of a regular polygon is 60.
 36060=6
Therefore, the given polygon is a hexagon.

(iv) If the interior angle is 108, then the exterior angle will be 72.                (interior and exterior angles are supplementary)
Sum of the exterior angles of a polygon is 360°.

Let there be n sides of a polygon.

72n=360n=36072n=5

Since it has 5 sides, the polygon is a pentagon.

(v) A pentagon has 5 diagonals.

 If n is the number of sides, the number of diagonals = n(n-3)25(5-3)2=5

Mathematics
RS Aggarwal (2016)
Standard VIII

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