Find the sum of the measures of the interior angles of each of the following convex polygons: a pentagon, an octagon, a dodecagon, a forty-sided polygon, a fifty-two sided polygon, a hundred sided polygon.

Answer:pentagon=540° octagon= 1080° decagon= = 1440° forty-sided polygon= 6840° fifty-two-sided polygon=9000° hundred-sided polygon=17640°Step-by-step explanation:To find the measure of the sum of the interior angle of a polygon, we will simple use the formula;sum of interior angle = (n-2)180where n is the number of sides of the polygonWe are ask to find the sum of the interior angle of a pentagon, octagon, decagon, a forty-sided polygon, a fifty-two-sided polygon and a hundred-sided polygon.First we need to define some terminology;A penatgon is a five(5)-sided polygonAn Octagon is an eight(8)-sided polygonA Decagon is a ten(10)-sided polygonWe can now proceed to solvesum of interior angle = (n-2)180Sum of interior angle of a pentagon = (5-2)180                                                              = 3 × 180                                                              =540°Sum of interior angle of a pentagon = 540°Sum of interior angle of an octagon  = (8-2)180                                                              = 6 × 180                                                              =1080°Sum of interior angle of an octagon = 1080°Sum of interior angle of a decagon  = (10-2)180                                                              = 8 × 180                                                              =1440°Sum of interior angle of a decagon = 1440°Sum of interior angle of a forty-sided polygon  = (40-2)180                                                                                = 38 × 180                                                                                 =6840°Sum of interior angle of a forty-sided polygon = 6840°Sum of interior angle of a fifty-two-sided polygon  = (52-2)180                                                                                     = 50 × 180                                                                                      =9000°Sum of interior angle of a fifty-two-sided polygon = 9000°Sum of interior angle of a hundred-sided polygon  = (100-2)180                                                                                      = 98 × 180                                                                                       =17640°Sum of interior angle of a hundred-sided polygon = 17640°