SOLUTION: A polygon has two interior angles of 120 degrees each and the others are 150 degrees.Calculate a. The number of sides of the polygon b. The sum of interior angles

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Question 1183295: A polygon has two interior angles of 120 degrees each and the others are 150 degrees.Calculate a. The number of sides of the polygon b. The sum of interior angles
Found 3 solutions by Plocharczyk, ikleyn, MathTherapy:
Answer by Plocharczyk(17)   (Show Source):
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A polygon has two interior angles of 120 degrees each and the others are 150 degrees.
240 + 150m = (n-2)180 where n = the number of sides and m = the number of 150° angles. The number of sides could be 5, then there would be 2 120^o interior angles, and 2 150° angles. The sum would be 540^o. The number of sides could be 10, then there would be 2 120^o interior angles, and 8 150° angles. The sum would be 1440^o. The number of sides could be 15, then there would be 2 120^o interior angles, and 14 150° angles. The sum would be 2340^o. The number of sides could be 20, then there would be 2 120^o interior angles, and 20 150° angles. The sum would be 3240^o. The number of sides could be 25, then there would be 2 120^o interior angles, and 26 150° angles. The sum would be 4140^o. The number of sides could be 30, then there would be 2 120^o interior angles, and 32 150° angles. The sum would be 5040^o. This list could go on and on forever. Edwin

Answer by ikleyn(52810)   (Show Source):
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Let "n" be the number of sides of the polygon (the same as the number of vertices). Two interior angles are 120 degrees each, and the other (the rest) (n-2) interior angles are 150 degrees each. Write equation for the sum of all interior angles 120 + 120 + (n-2)*150 = (n-2)*180. Simplify and find "n" 240 + 150n - 300 = 180n - 360 240 + 360 - 300 = 180n - 150n 300 = 30n n = 300/30 = 10. Thus the polygon has 10 sides and 10 vertices. The sum of the interior angles is (10-2)*180 = 8*180 = 1440 degrees. ANSWER

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Answer by MathTherapy(10555)   (Show Source):
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A polygon has two interior angles of 120 degrees each and the others are 150 degrees.Calculate a. The number of sides of the polygon b. The sum of interior angles

Since 2 interior angles measure 120^o each, then 2 exterior angles measure 180^o - 120^o = 60^o each Let number of angles (exterior/interior), be n With 2 angles known, remaining angles = n - 2 Since remaining interior angles measure 150^o each, remaining exterior angles measure 180^o - 150^o = 30^o each. So, remaining exterior angles measure a total of 30(n - 2) = 30n - 60 With all exterior angles measuring 120^o and (30n - 60)^o, and since the exterior angles of any polygon sum to 360^o, we now have: 120 + 30n - 60 = 360 60 + 30n = 360 30n = 300 Number of sides, or Sum of interior angles: OR Two (2) interior angles measure 120^o each, so 2 interior angles measure 2(120)^o Let number of angles (exterior/interior), be n With 2 interior angles known, remaining angles = n - 2 Since remaining interior angles measure 150^o each, remaining interior angles measure 180(n - 2)^o With all interior angles measuring 2(120)^o and 150(n - 2)^o, and since the interior angles of any polygon sum to 180(n - 2)^o, we now have: 2(120) + 150(n - 2) = 180(n - 2) 240 = 180(n - 2) - 150(n - 2) 240 = 30(n - 2) Number of sides, or Sum of interior angles: