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# Regular pentagon P has all five diagonals drawn. What is th

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Regular pentagon P has all five diagonals drawn. What is th [#permalink]  26 Oct 2017, 23:39
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Regular pentagon P has all five diagonals drawn. What is the angle between two of these diagonals where they meet at a vertex of the pentagon?

(A) 12°

(B) 36°

(C) 54°

(D) 60°

(E) 72°

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Re: Regular pentagon P has all five diagonals drawn. What is th [#permalink]  27 Oct 2017, 04:51
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Let's start from the fact that the sum of interior angles of a regular polygon is always computed as $$(n-2)*180°$$, where n is the number of sides. Thus, the sum of interior angles of a pentagon is 3*180 = 540°, so that, because it is regular, each of its angles is 108° (540/5).

Then, at a vertex where two diagonals meet, the angle is divided in three equal portions, so that the angle between the two diagonals measures 108/3 = 36°.

Re: Regular pentagon P has all five diagonals drawn. What is th   [#permalink] 27 Oct 2017, 04:51
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# Regular pentagon P has all five diagonals drawn. What is th

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