Question

Find the degree and radian measure of
exterior and interior angle of a regular
i) Pentagon
ii) Hexagon
iii) Septagon
iv) Octagon ​

Answer 1

Step-by-step explanation:

Pentagon : exterior angle = 72° or 2π / 5 and interior angle= 108° or 3π / 5.

Hexagon : exterior angle = 60° or π / 3 and interior angle= 120° or 2π/ 3.

Septagon : exterior angle = (360° / 7) or 51.42° or 2π / 7 and interior angle= 900° / 7 or 128.57° or 5π / 7 .

Octagon : exterior angle = 45° or π / 4 and interior angle= 135° or 3π / 4 .

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Answer 2

Answer:

Sum of the interior angles of n-sided polygon

=

${(n - 2)\pi}$

in Pentagon

n = 5

so,

(5 - 2)π

3π

each interior angle of Pentagon =

$\frac{3\pi}{5}$

so radian =

$\frac{3\pi}{5}$

In degree

$\frac{3\pi}{5} \times \frac{180 }{\pi}$

= 108°

sum of exterior angles = 360°

$\frac{sum \: of \: all \: exterior \: angles}{no. \: of \: angles}$

$\frac{360}{5}$

=72°

In Hexagon

n = 6

sum of interior angles in radian = (n-2)π

(6-2)π

4π

each interior angle of hexagon in radian =

$\frac{4\pi}{6}$

In degree

$\frac{4\pi}{6} \times \frac{180}{\pi}$

220°

Hence,

each exterior angle = 360°/6

= 60°

In septagon

n = 7

sum of interior angles in radian = (n-2)π

(7-2)π

5π

each interior angle of septagon in radian =

$\frac{5\pi}{7}$

In degree

$\frac{5\pi}{7} \times \frac{180}{\pi}$

about 128.57°

Hence,

each exterior angle =360°/7

approximately 51.43°

In octagon

n = 7

sum of interior angles in radian = (n-2)π

(8-2)π

6π

each interior angle of octagon in radian =

$\frac{6\pi}{8}$

In degree

$\frac{6\pi}{8} \times \frac{180}{\pi}$

= 135°

Hence,

exterior angle =

$\frac{sum \: of \: all \: angles}{no. \: of \: angles}$

$= \frac{360}{8}$

$= 45$