document.write( "Question 1201837: Two of three consecutive sides of regular nonagon(nine sided) are produced to meet at point T. Calculate the size of the angle formed at T. \n" ); document.write( "
Algebra.Com's Answer #836374 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Answer: 100 degrees\r
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\n" ); document.write( "\n" ); document.write( "Explanation:\r
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\n" ); document.write( "\n" ); document.write( "A regular polygon has equal angles and equal sides. \r
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\n" ); document.write( "\n" ); document.write( "Let's draw out a regular nonagon with 9 sides.
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\n" ); document.write( "\n" ); document.write( "Highlight 3 consecutive sides.
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\n" ); document.write( "These are adjacent neighboring sides.
\n" ); document.write( "I picked the 3 sides at the bottom marked in red.\r
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\n" ); document.write( "\n" ); document.write( "Pick two sides, of those 3, that aren't neighbors. Extend them until they meet at point T.
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\n" ); document.write( "\n" ); document.write( "We'll need to know the measure of each interior angle for a regular nonagon.
\n" ); document.write( "S = sum of interior angles of a polygon of n sides
\n" ); document.write( "S = 180(n-2)
\n" ); document.write( "S = 180(9-2)
\n" ); document.write( "S = 180*(9-2)
\n" ); document.write( "S = 1260
\n" ); document.write( "Then we divide that into nine equal pieces
\n" ); document.write( "1260/9 = 140
\n" ); document.write( "The measure of each interior angle of a regular nonagon is 140 degrees.\r
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\n" ); document.write( "Each adjacent pair of angles marked 140 and x are supplementary.
\n" ); document.write( "They add to 180 degrees to form a straight line.
\n" ); document.write( "x+140 = 180
\n" ); document.write( "x = 180-140
\n" ); document.write( "x = 40\r
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\n" ); document.write( "\n" ); document.write( "Focus on the triangle at the very bottom. The three interior angles add to 180.
\n" ); document.write( "x+x+T = 180
\n" ); document.write( "40+40+T = 180
\n" ); document.write( "80+T = 180
\n" ); document.write( "T = 180-80
\n" ); document.write( "T = 100 is the final answer.
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