Question

Using the sum of exterior angles = 360 degrees of a polygon find the measure of interior polygon of :
i. a regular octagon
ii. a regular 20-gon


Anyone will answer i will mark brainliest. PLS PLZ PLS PLZ

Answer 1

Answer:

$(i)135 {}^{0} each \: and \: \: sum = 1080 {}^{0}$

$(ii)each \: 162 {}^{0} and \: \: sum = 3240 {}^{0}$

Step-by-step explanation:

(¡) Since it is a regular octagon,each exterior angle is 360deg ÷ 8 = 45 deg.

We know that sum of an exterior and it's adjacent interior angle of a polygon is = 180deg.

So , One of the interior angle = 180deg- 45deg

= 135deg

Since all the interior angles are equal in measure,

So, the sum of the interior angles of regular octagon is = 135×8deg

= 1080 deg

(¡¡) Each exterior angle of a regular 20- gon is

$= 360 {}^{0} \div 20$

$= 18 {}^{0}$

Now, Sum of an exterior angle and it's adjacent interior angle is 180 deg. So, one interior angle of the 20-gon

$= 180 {}^{0} - 18 {}^{0}$

$= 162 {}^{0}$

Since all the interior angles of a 20-gon are equal, So the sum of the interior angles of regular 20-gon is

$= 162 {}^{0} \times 20$

$= 3240 { }^{0}$