document.write( "Question 63106: suppose that the interior angles of a convex pentagon are five consecutive numbers. what is the measure of the larghtst angle? \n" ); document.write( "

Algebra.Com's Answer #43956 by joyofmath(189) $\"\"$ $\"About$

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suppose that the interior angles of a convex pentagon are five consecutive numbers. what is the measure of the largest angle?\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "So, we're looking for 5 consecutive numbers that add up to 540.
\n" ); document.write( "So, $\"x%2B%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%2B%28x%2B4%29+=+540\"$ .
\n" ); document.write( "Combine the x's and the constants and you get $\"5x%2B10=540\"$ .
\n" ); document.write( "Subtract 10 from each side: $\"5x=530\"$ .
\n" ); document.write( "So, $\"highlight%28x=106%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "So, the five angles are 106, 107, 108, 109, and 110.
\n" ); document.write( "Note that these five numbers do add up to 540 and are consecutive.\r
\n" ); document.write( "\n" ); document.write( "So, the answer to the question, what is the largest angle, is $\"highlight%28110%29\"$ . \n" ); document.write( "

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