Question 63106: suppose that the interior angles of a convex pentagon are five consecutive numbers. what is the measure of the larghtst angle?
Answer by joyofmath(189)   (Show Source):
You can put this solution on YOUR website! suppose that the interior angles of a convex pentagon are five consecutive numbers. what is the measure of the largest angle?
The angles in a pentagon add up to 540 degrees. In general, an n-sided polygon has angles that add up to 180*(n-2) where n is the number of sides.
So, we're looking for 5 consecutive numbers that add up to 540.
So,  .
Combine the x's and the constants and you get  .
Subtract 10 from each side:  .
So,  .
So, the five angles are 106, 107, 108, 109, and 110.
Note that these five numbers do add up to 540 and are consecutive.
So, the answer to the question, what is the largest angle, is  .
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