SOLUTION: four of the angles of a pentagon have measures 30,60,120, and 165. find the measure of the fifth angle.

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Question 267542: four of the angles of a pentagon have measures 30,60,120, and 165. find the measure of the fifth angle.
Answer by vksarvepalli(154) About Me  (Show Source):
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sum of all the angles(interior) of a n sided polygon is given by

sum = 180(n-2) degrees
since pentagon has 5 sides (n=5)
sum of all the angles=180(5-2)=180*3 = 540 degrees
given four of the angles measure 30,60,120, and 165
let the fifth angle be x
so 30+60+120+165+x=540 => 375+x=540
thus x=165 degrees
so the fifth angle measures 165 degrees