document.write( "Question 1153977: The ratio of the angle measures in a parallelogram are 2:3:2:3. Find the measure of the following angles: \n" ); document.write( "

Algebra.Com's Answer #776325 by ramkikk66(644) $\"\"$ $\"About$

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\n" ); document.write( "The sum of all the angles of a polygon having n sides (n >= 3) is given by
\n" ); document.write( " $\"%282n+-+4%29+%2A+90\"$ degrees.\r
\n" ); document.write( "\n" ); document.write( "The sum of all the angles of a parallelogram (which has 4 sides) is
\n" ); document.write( "4 * 90 = 360 degrees\r
\n" ); document.write( "\n" ); document.write( "The angles are in the ratio 2:3:2:3
\n" ); document.write( "So if we assume the first angle is 2x, the other angles are 3x, 2x and 3x. (As you know, opposite angles of a parallelogram are equal)\r
\n" ); document.write( "\n" ); document.write( "So sum of the angles -
\n" ); document.write( " $\"2x+%2B+3x+%2B+2x+%2B+3x+=+10x+=+360\"$
\n" ); document.write( "Solving, $\"x+=+36\"$ \r
\n" ); document.write( "\n" ); document.write( "Hence the 4 angles are 2x, 3x,2x, 3x i.e.
\n" ); document.write( " $\"72\"$ , $\"108\"$ , $\"72\"$ and $\"+108+\"$ degrees\r
\n" ); document.write( "\n" ); document.write( "Check: Sum = 72 + 108 + 72 + 108 = 360. Confirmed.\r
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