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# Decagon angle

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A decagon has interior angle measures of 156, 178, 124, 132, 138, 142, 116, 178, and 159. Find the measure of the missing angle. (Show work) please and thanks!

Mar 23, 2019
edited by Guest  Mar 23, 2019

#1
+6

I beilive I have heard that  a decagon equals 1440 degree's what you can do lets see you have 9 angles degree mesaurments on here add them then subtract the sum from 1440 after that your diffrence will be your answer.....

like this

\(156 + 178 + 124 +132 +138+142+116+178 +159 = sum\)

\( 1440 - sum = difference \)

Mar 23, 2019
edited by HiylinLink  Mar 23, 2019
edited by HiylinLink  Mar 23, 2019
edited by HiylinLink  Apr 5, 2019
edited by HiylinLink  Apr 5, 2019

#1
+6

I beilive I have heard that  a decagon equals 1440 degree's what you can do lets see you have 9 angles degree mesaurments on here add them then subtract the sum from 1440 after that your diffrence will be your answer.....

like this

\(156 + 178 + 124 +132 +138+142+116+178 +159 = sum\)

\( 1440 - sum = difference \)

edited by HiylinLink  Mar 23, 2019
edited by HiylinLink  Mar 23, 2019
edited by HiylinLink  Apr 5, 2019
edited by HiylinLink  Apr 5, 2019
#2
+1

The formula for the sum of the angles of an n-gon (in this case, a 10-gon), is 180(n - 2). So, the sum of the angles is 1440. Now, we just calculate 1440 - (156 + 178 + 124 + 132 + 138 + 142 + 116 + 178 + 159) = 1440 - 1323 = 117.

Hoping this helped,

asdf334

Mar 23, 2019