Question

how many diagonals are there in decagon​

Answer 1

Step-by-step explanation:

here's your answer

35 diagonals

• 1. How many diagonals of a regular decagon (a 10 sided polygon) are not parallel to any of the sides (AMC12)? A decagon has (10 2) – 10 = 35 diagonals. Each pair of opposing sides has three diagonals which are parallel to them, so 5*3 = 15 of the diagonals are parallel to a side.

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Answer 2

Answer:

A decagon has 10 vertices, by definition (deka is Greek for ‘ten’).

Every vertex can be joined to the other 9 vertices. Two of the 9 resulting straight line segments, viz. the ones joining that vertex to the next vertex on the left and on the right, are sides of the decagon. The other 7 are diagonals.

Are there, then, 10 times 7 = 70 diagonals? No, because each diagonal has been counted twice (once starting with one of its ends and one starting with the other.) There are therefore ½ of 70, i.e. 35 diagonals in a decagon.

Generally, a polygon with n sides has ½n(n-3) diagonals: none for a triangle, 2 for a quadrilateral, 5 for a pentagon, 9 for a hexagon etc.

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