8. How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

(a) 21

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(b) 170

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(d) 357

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Solution

The correct option is B (b) 170
Ans: (b)
Sol: We have 20 vertices linking to 17 others each: that is 17*20=340. We divide that by 2 since every diagonal connects two vertices. 340/2=170. The vertex that does not connect to any diagonal is just not counted.

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