Let X be the set of all even positive integers n such that the measure of the angle of some regular

Question

Let X be the set of all even positive integers n such that the measure of the angle of some regular polygon is n degrees. Find the number of elements in X.

Accepted Answer

{"content":[{"type":"paragraph","content":[{"text":"Step 1:","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" Let number of sides of polygon be P."}]},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 2:","type":"text"},{"text":" ( P – 2) .180°","type":"text"}]},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" =>                      = n°","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"text":" then P(180 – n) = 360","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 5:","type":"text"},{"text":" But ","type":"text"},{"type":"math_inline","attrs":{"latex":"n"}},{"text":" = 2k then P =","type":"text"}]},{"content":[{"marks":[{"type":"bold"}],"text":"Step 6:","type":"text"},{"text":" Hence possible values of (90 – k) are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45 and 60","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 7:","type":"text"},{"type":"text","text":" =>    16 such polygons are possible."}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

Solution