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 06-22-2012, 12:13 AM #2 byahnoob Member   Join Date: Aug 2011 Posts: 348 This question was asked previously many times... i take no credit for this but i found this helpful The shown figure is a quadrilateral (4 sides), so the sum of all its angles' measures is 360 degrees. x+y = 80 So the sum of the other 2 angles' measures is 360 - 80, or 280. Since the other 2 angles have equal measures (as stated in the problem), the measures must be 140. DOING IT BY HAND: Regular 3-sided shapes have 60 degree angles - 180 in total Regular 4-sided shapes have 90 degree angles - 360 in total Regular 5-sided shapes have ___ degree angles - 540 in total Regular 6-sided shapes have ___ degree angles - 720 in total Regular 7-sided shapes have ___ degree angles - 900 in total Regular 8-sided shapes have ___ degree angles - 1080 in total Regular 9-sided shapes have ___ degree angles - 1260 in total 140 is the total divided by the number of sides (1260/9), so the answer is 9 sides You keep adding 180 as the total number of sides increases by 1 DOING IT BY EQUATION: sum of all angles' measures =180(n-2), where n = number of sides 180(3-2)=180 180(4-2)=360 180(5-2)=540 180(6-2)=720 180(7-2)=900 180(8-2)=1080 180(9-2)=1260 9 angles of 140 degrees each = 1260 Reply