Math, asked by babajikijai13213, 1 month ago

what is the number of diagonals in a polygon of 12 sides and 20 sides​

Answers

Answered by awesome12805
2

Answer:

54 sides as ×- y = 54 because their are 12 and 20 sides

Answered by itzsecretagent
8

Answer:

\sf\small{ \underline{\underline{ \pmb{In  \: first \:  condition:-}}}}

A closed polygon with 12 sides will have 12 vertices.

A diagonal requires two vertices.

=> C(12,2)= 12!/2! 10!= 66 lines can be drawn using any 2 points.

  • But 12 lines form the sides of the polygon.

 \sf \: Number \:  of  \: diagonals = nC_2 – n

 \sf \implies \: 12C_2 – 12

 \sf \implies \:  66  - 20

 \sf \implies \: 54 \:  ways

\sf\small{ \underline{\underline{ \pmb{In  \: second  \: condition:-}}}}

A closed polygon with 20 sides will have 20 vertices.

A diagonal requires two vertices.

=> C(20,2)= 20!/2! 10!= 190 lines can be drawn using any 2 points.

  • But 20 lines form the sides of the polygon.

 \sf \: Number  \: of  \: diagonals = nC_2 – n

 \sf \implies \: 20C_2 – 20

 \sf \implies \: 190 - 20

 \sf \implies \: 170 \:  ways

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