Question

Find the sum of measures of all the interior angles of a polygon with
(i) 7 sides
(ii) 9 sides.​

Answer 1

Answer:

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(i) The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.

sum of angles = (n - 2) × 180

sum of angles = (7 - 2) × 180

sum of angles = 5 ×180

(ii) A nonagon can have 6 diagonals drawn inside of it to form 7 interior triangles.

Every triangle's angles have a sum of 180˚. Therefore, since there are 7

triangles, the sum of the interior angles in a nine-sided polygon is

7×180˚=1260˚

This can be generalized to a polygon with n sides, since n−2

triangles can be drawn in any polygon. Thus, the formula is

180˚(n−2).

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Answer 2

formula - (n-2) × 180

Step-by-step explanation:

by this method u can calculate

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