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. (ii) Sum of the interior angles of a regular hexagon = $\left(6-2\right)×{180}^{\circ }={720}^{\circ }$ (iii) Each exterior angle of a regular polygon is ${60}^{\circ }$. Therefore, the given polygon is a hexagon. (iv) If the interior angle is ${108}^{\circ }$, then the exterior angle will be ${72}^{\circ }$.                (interior and exterior angles are supplementary) Sum of the exterior angles of a polygon is 360°. Let there be n sides of a polygon. $72n=360\phantom{\rule{0ex}{0ex}}n=\frac{360}{72}\phantom{\rule{0ex}{0ex}}n=5$ Since it has 5 sides, the polygon is a pentagon. (v) A pentagon has 5 diagonals.  MathematicsRS Aggarwal (2016)Standard VIII

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