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)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Answer: 100 degrees\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Explanation:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A regular polygon has equal angles and equal sides. \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Let's draw out a regular nonagon with 9 sides. \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Highlight 3 consecutive sides. \n" ); document.write( " \n" ); document.write( "These are adjacent neighboring sides. \n" ); document.write( "I picked the 3 sides at the bottom marked in red.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Pick two sides, of those 3, that aren't neighbors. Extend them until they meet at point T. \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \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. \n" ); document.write( " \n" ); document.write( " |