The internal angles of a plane polygon are in AP. The smallest angle i

1.	The internal angles of a plane polygon are in AP. The smallest angle is 100° and the common difference is 10°. Find the number of sides of the polygon.
Answer» Smallest interior angle = 100, largest exterior angle= 180 − 100 =80 Similarly other exterior angles are 70, 60, 50, …. Sum of all the exterior angles = 360 So n(2.80 +(n-1)(-10))/2 = 360 or n(17 − n) = 72 We can see that the above equation is true for both n = 8, 9. But for n = 9, the 9^thexterior angle must be 0 which is not possible so only 8 is possible.

The internal angles of a plane polygon are in AP. The smallest angle is 100° and the common difference is 10°. Find the number of sides of the polygon.

Answer»

Smallest interior angle = 100, largest exterior angle= 180 − 100 =80

Similarly other exterior angles are 70, 60, 50, ….

Sum of all the exterior angles = 360

So n(2.80 +(n-1)(-10))/2 = 360 or n(17 − n) = 72

We can see that the above equation is true for both n = 8, 9. But for n = 9, the 9^thexterior angle must be 0 which is not possible so only 8 is possible.

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The internal angles of a plane polygon are in AP. The smallest angle is 100° and the common difference is 10°. Find the number of sides of the polygon.

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