Question

Q.For d given regular octagon,find:
a)measure of each interior angle
b)measure of each exterior angle
c)Sum of measure of exterior angle​

Answer 1

Answer -

»Given:

figure is a octagon.

» To find:

a)measure of each interior angle

b)measure of each exterior angle

c)Sum of measure of exterior angle

» Solution -

a)measure of each interior angle.

we know that,

${\boxed{\boxed{\pink{Sum \:of\:all\:interior\:angles\:of\:n- sided\:polygon = 180(n-2)}}}}$

given:

n = 8

sum of total angles of polygon = 180(8-2)

= 180×6

= 1080°

We know that in a regular polygon all angles are equal.

so an individual angle of octagon =

$\frac{sum\: of \:all\: interior\: angles}{8(number\:of\:sides)}$

= 1080/8

= 135°.

${\boxed{\boxed{\purple{Measure\:of\:each\:interior\:angle\:of\:regular\:ocatgon = 135^{\circ}}}}}$

b) measure of each exterior angle.

we know that,

sum of exterior angles of regular polygon = 360°.

therefore,

each exterior angle = $\small\frac{360^{\circ}}{number\: of\:sides\:in\:polygon}$

= 360/8

= 45°.

c) Sum of measure of exterior angle = 360°

as sum of exterior angles of any regular polygon is equal to 360°.