AMC 10A/12A 2026 (Problem 4/3)Half of the internal angles of a polygon measure 150∘150^\circ150∘ each, and the other half of its internal angles measure 190∘190^\circ190∘ each. How many sides does the polygon have?(A) 36\text{(A)}\;36(A)36(B) 40\text{(B)}\;40(B)40(C) 60\text{(C)}\;60(C)60(D) 72\text{(D)}\;72(D)72(E) 180\text{(E)}\;180(E)180Related TopicsCoreRegular PolygonsCheck AnswerYour answer:ABCDECheckHints (2)Hint 1Let 2n2n2n be the number of sides of the polygon.Sum of the angles=180∘(2n−2)\text{Sum of the angles}=180^\circ(2n-2)Sum of the angles=180∘(2n−2)Hint 2150∘n+190∘n=180∘(2n−2)150^\circ n+190^\circ n=180^\circ(2n-2)150∘n+190∘n=180∘(2n−2)340∘n=360∘(n−1)340^\circ n=360^\circ(n-1)340∘n=360∘(n−1)17n=18n−1817n=18n-1817n=18n−18n=18n=18n=18Answer=2n=36\text{Answer}=2n=36Answer=2n=36Final Answer(A) 36Related Problems (2)AMC 12B 2024 (Problem 23)AMC 10B/12B 2023 (Problem 25)