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# Find the Magnitude, in Radians and Degrees, of the Interior Angle of a Regular Pentagon. - Mathematics

Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.

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#### Solution

$\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi$
Number of sides in the pentagon = 5
$\therefore \text{ Sum of the interior angles of the pentagon }= \left( 5 - 2 \right)\pi = 3\pi$
$\text{ Each angle of the pentagon }= \frac{\text{Sum of the interior angles of the polygon}}{\text{Number of sides}} = \frac{3\pi}{5}\text{ rad }$
$\text{ Each angle of the pentagon }= \left( \frac{3\pi}{5} \times \frac{180}{\pi} \right)^\circ= 108^\circ$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 5.1 | Page 15
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