Question

In n )
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

Answer:

10

Step-by-step explanation:

I have attached below the solution

hope this helps you

pls mark as brainliest answer

follow me on brainly

Answer 2

Answer :

➥ A polygon has 10 sides

Given :

➤ The interior angle of a regular polygon exceeds its exterior angle by 108°

To Find :

➤ A polygon have how many sides ?

Solution :

We are given that the interior angle of a regular polygon exceeds it's exterior angle by 180°.

So ,

Interior angle = x + 108

Sum of interior angle is 108°

$\tt{:\implies x + x + 108 = 180\degree}$

$\tt{: \implies 2x + 108 = 180}$

$\tt{: \implies 2x = 180 - 108}$

$\tt{: \implies 2x = 72}$

$\tt{: \implies x = \cancel{\dfrac{72}{2} }}$

$\bf{: \implies \underline{ \: \: \underline{ \green{ \: \: x = 36 \: \: }} \: \: }}$

Now ,

$\tt{:\implies Each \: exterior \: angle = \dfrac{360}{n}}$

$\tt{:\implies 36 = \dfrac{360}{n}}$

$\tt{:\implies n = \cancel{\dfrac{360}{36}}}$

$\bf{:\implies \underline{ \: \: \underline{ \purple{ \: \: n = 10 \: \: }} \: \: }}$

Hence, a polygon has 10 sides.