Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

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

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

#### Solution

$\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi$
Number of sides in the heptagon = 7
$\therefore\text{ Sum of the interior angles of the heptagon }= \left( 7 - 2 \right)\pi = 5\pi$
$\text{ Each angle of the heptagon }= \frac{\text{ Sum of the interior angles of the polygon}}{\text{ Number of sides}} = \frac{5\pi}{7}\text{ rad }$
$\text{Each angle of the heptagon }= \left( \frac{5\pi}{7} \times \frac{180}{\pi} \right)^\circ= \left( \frac{900}{7} \right)^\circ= 128^\circ 34'17 ''$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 5.3 | Page 15