Question

Find the value of each interior angles of a regular polygon having :-
5sides
8sides
15 sides

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Answer 1

What the Question Says :

We have to find the value of each interior angle of a regular polygon :

Given sides :

• 5
• 8
• 15

To find the value of each interior angle of a polygon we apply : $\sf\dfrac{(2n-4)}{n}\times{90^{\circ}}$

★Solution 1 :

• 5 sides

So, substituting the formula we get ,

Interior angles of a polygon having 5 sides

$\sf=\dfrac{(2\times5-4)}{5}\times{90^{\circ}}$

$\sf=\dfrac{(10-4)}{5}\times{90^{\circ}}$

$\sf=\dfrac{(6)}{\cancel{5}^1}\times{\cancel{90}^{\circ}}^{18}$

$\sf={6\times18^{\circ}=108^{\circ}}$

★Solution 2 :

• 8 sides

Interior angles of a polygon having 8 sides

$\sf=\dfrac{(2\times8-4)}{8}\times{90^{\circ}}$

$\sf=\dfrac{(16-4)}{8}\times{90^{\circ}}$

$\sf=\dfrac{\cancel{12}^3}{\cancel8^2}\times{90^{\circ}}$

$\sf=\dfrac{3}{\cancel{2}^1}\times{\cancel{90^{\circ}}^{45}}$

$\sf={3\times45^{\circ}=135^{\circ}}$

★Solution 3 :

• 15 sides

Interior angles of a polygon having 15 sides

$\sf=\dfrac{(2\times15-4)}{15}\times{90^{\circ}}$

$\sf=\dfrac{(30-4)}{15}\times{90^{\circ}}$

$\sf=\dfrac{26}{\cancel{15}^1}\times{\cancel{90^{\circ}}^6}$

$\sf={26\times6^{\circ}=156^{\circ}}$

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