document.write( "Question 192078: The sum of the measures of three of the interior angles of a convex pentagon is 280. The measure of the fourth angle is three times the measure of the fifth angle. Fin the measure of the fourth angle. \n" ); document.write( "
Algebra.Com's Answer #144135 by orca(409)\"\" \"About 
You can put this solution on YOUR website!
Note that the sum of the measures of the angles of a n-gon is 180(n-2).
\n" ); document.write( "So the sum of the measures of the angles of a pentagon is 180(5-2)=540.\r
\n" ); document.write( "\n" ); document.write( "As the sum of the measures of the first three angles is 280 degrees, the sum of the measures of the the fourth angle and the fifth angle is 540 - 280 = 260 degrees.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let x represent the measure of the fifth angle, then the fourth angle is 3x.
\n" ); document.write( "As we have already known their sum is 260, we can set up an equation:
\n" ); document.write( "x + 3x = 260
\n" ); document.write( "Solving for x, we have:
\n" ); document.write( "4x = 260
\n" ); document.write( "x = 65\r
\n" ); document.write( "\n" ); document.write( "So the 5th angle is 65 degrees
\n" ); document.write( "the 4th angle is 3x = 3*65 = 195 degrees.
\n" ); document.write( " \n" ); document.write( "
\n" );