Question

If the ratio of the number of sides of a polygon to the number of diagnols is 2:5 , then the sum of the angles of the polygon

Answer 1

Answer:

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Answer 2

Answer:

What does “the number of a polygon” mean? Did you mean the number of sides? I’ll assume so.

n= number of sides

Since polygon has n sides, it has n vertices.

For each vertex, the number of diagonals from that vertex =n−3

(we do not count the vertex itself, or the 2 vertices adjacent to it).

This makes for a total of n(n−3) . However, we have counted each diagonal twice (once from each endpoint).

So the total number of diagonals =12n(n−3)

Ratio of number of sides to number of diagonals =2:5

n12n(n−3)=25

n(n−3)=5n

n−3=5

n=8

Sum of angles =180(n−2)=180(6)=1080

Step-by-step explanation:

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