SOLUTION: Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?

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Question 148511: Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?




Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
The angles of a pentagon add up to 540. I f they are all consecutive, and they add up to 540, then:

x+(x+1)+(x+2)+(x+3)+(x+4)=540

Combine like terms and get
5x+10=540

Subtract 10 from each side
5x=530

Divide both sides by 5
x=106

The largest angle is x+4. 106+4=110.
So it is 110 degrees.