Question 810912: how to solve the value of the angle formed by two diagonals of a regular pentagon?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! each interior angle of a pentagon is 108 degrees.
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since a pentagon's diagonal forms an isosceles triangle with its vertex angle being one of the pentagon's 108 degree interior angles, the sum of the base angles of the isosceles triangle must be 180 - 108 = 72 degrees.
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since the base angles of any isosceles triangle are congruent, each base angle must be 72/2 = 36 degrees.
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let's call the base angles B.
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each vertex of a pentagon will have two diagonals intercepting it, and forming angles B with the sides of the pentagon at that vertex.
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so each included angle of a pentagon is made up of two angles B (each angle B is 36 degrees) and a central angle also 36 degrees, like so: 36*3 = 108 degrees.
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so the angle formed by two diagonals of a regular pentagon is 36 degrees.
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