Question

a 32 sided polygon with equal angles,how much is each of its angle (inner and outer angles)​

Answer 1

$\bf\large\underline{\underline{ Given :- }}$

• 32 sided polygon

• polygon is regular sided

$\bf\huge\underline{\underline{ To \: Find:- }}$

• inner angle

• outer angle

$\bf\huge\underline{\underline{ Answer :- }}$

$\boxed{ \large\bf\red{ sum \: of \: angles = (n - 2) × 180}}$

SUM OF INNER ANGLE

• n = 32

• $\red{ \implies}$ sum = ( 32 - 2) × 180

• $\red{ \implies}$ sum = 30 × 180

• $\red{ \implies}$ sum = 5400 °

$\rule{10cm}{0.05cm}$

INNER ANGLE

• each inner angle = sum / number of sides

• $\red{ \implies}$each inner angle = 5400 / 32

• $\red{ \implies}$each inner angle = 168.75°

$\rule{10cm}{0.05cm}$

OUTER ANGLE

• $\red{ \implies}$outer angle = 180 - inner angle

• $\red{ \implies}$outer angle = 180 - 168.75

• $\red{ \implies}$outer angle = 11.25 °

$\rule{10cm}{0.05cm}$

$\rule{10cm}{0.05cm}$

$\rule{10cm}{0.05cm}$