Question

6. What is the measure of each exterior angle

of a regular decagon?
a.45°
B.36°
C. 30°
d. 40°

Answer 1

It is 36 degrees because the out side is equal to 360 degrees

If you divide that by ten you get 36 for each angle

Explanation:

Answer 2

• 36° .

⠀

Explanation :

⠀

For a regular polygon of n sides, we have

`\bf \longrightarrow \qquad Each \: exterior \: angle = { \bigg( {(360)/(n) } \bigg)}^( \circ)`

⠀

Here, We are to find the measure of each exterior ange of a regular decagon.

⠀

• So, we know a regular decagon has 10 sides, so n = 10 .

⠀

Now, substituting the value :

⠀

`\sf \longrightarrow \qquad Each \: exterior \: angle_((Decagon)) = { \bigg( {(360)/(10) } \bigg)}^( \circ)`

⠀

`\sf \longrightarrow \qquad Each \: exterior \: angle _((Decagon))= { \bigg( {(36 \cancel0)/(1 \cancel0) } \bigg)}^( \circ)`

⠀

`\sf \longrightarrow \qquad Each \: exterior \: angle_((Decagon)) = { \bigg( {(36)/(1) } \bigg)}^( \circ)`

⠀

`\pmb{\bf \longrightarrow \qquad Each \: exterior \: angle_((Decagon)) = 36^( \circ) }`

⠀

Therefore,

• The measure of each exterior angle of a regular decagon is 36° .