Question

14. The interior angle of a regular polygon exceeds its exterior angle by 108°. How many sides
does the polygon have?
(a) 16
(b) 14
(c) 12
(d) 10
​

Answer 1

${\huge {\underline {\mathfrak {\green{Answer}}}}}$

d) 10 is correct option

${\huge {\underline {\mathfrak {\green{Explanation:-}}}}}$

${\boxed {\red {\bf {Given:-}}}}$

Interior Angle = Exterior angle + 108°

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${\boxed {\red {\bf {Find:-}}}}$

No. of sides in the polygon = ?

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${\boxed {\red {\bf {Solution:-}}}}$

Let the exterior angle = x

We are given that the interior angle of a regular polygon exceeds its exterior angle by 108°

So, interior Angle = x + 108°

Since we know that the sum of interior angle and exterior angle is 180°

So,

= Exterior angle + Interior angle = 180°

= x + ( x + 108° ) = 180°

= 2x + 108° = 180°

= 2x = 180° - 108°

= x = $\frac{72}{36}$

= x = 36°

Thus, the interior angle

= x + 108°

= 36° + 108°

= 144°

Now,

To find the number of sides in the polygon

Using Formula,

= $180 × \frac {n-2}{n}$= Interior Angle

= $180 × \frac {n-2}{n}$= 144°

= n = 10

Hence the polygon has 10 sides

${\underline {\blue {Clearly \: option\:d) \:is\:correct }}}$

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Answer 2

hope it helps!

#sumedhian ❤❤