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What is the general formula to count the sum of all the interior angles of a polygon with ‘n’ number of sides?(a) 180°(b) 360°(c) 90°(d) 720°I got this question during a job interview.My question is based upon Quadrilaterals topic in portion Quadrilaterals of Mathematics – Class 8

Answer»

Right CHOICE is (a) 180°

For explanation: The general formula for the sum total of all the INTERIOR ANGLES of any POLYGON is (n-2)180°. For example: As we know that the sum of all the interior angles of any triangle is 180°.

So, now we can recheck it with the above formula. Sum of interior angles=(n-2)180°

Any triangles have three SIDES so n=3.

∴ Sum of interior angles=(3-2)180°

∴ Sum of interior angle=180°.



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