Question

Prove that the interior angle of a regular pentagon is three times the exterior angle of a decagon​

Answer 1

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Given Question:-

Prove that the interior angle of a regular pentagon is three times the exterior angle of a decagon​.

Required Answer:-

Yes! Interior angle of pentagon is three times exterior angle of a decagon.

Lets Prove!

Each interior angle of a pentagon-

• Formula:-  $\implies \rm \frac{(n-2)\times 180^\circ }{n}$ where n is number of sides.

$\implies \rm \frac{(5-2)\times 180^\circ }{5}$

$\implies \rm \frac{3\times 180^\circ }{5}$

$\implies \rm 108^\circ$

So, each interior angle of a pentagon in 108°.

So Now!

As we know,

Sum of exterior angles of  every polygon is 360°.

• Sides of decagon- 10

$\implies \rm \frac{360}{10} =36^\circ$

$\implies \rm 3\times 36=108^\circ$

$\huge{\boxed{\rm{\orange{Hence\: Proved!}}}}{\green{\checkmark}}$

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