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1. How many diagonals can be drawn in a pentagon?

Solution:
A pentagon has 5 sides. We obtain the diagonals by joining the vertices in pairs.
Total number of sides and diagonals,
= 5C2
= 5×42×1
= 5 × 2 = 10
This includes its 5 sides also.
⇒ Diagonals = 10 – 5 = 5
Hence, the number of diagonals
= 10 – 5
= 5

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