A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercise, determine the number of diagonals for the given polygon. B Diagonal D. octagon (8 sides)

A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercise, determine the number of diagonals for the given polygon. B Diagonal D. octagon (8 sides)

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter2: Parallel Lines

Section2.CT: Test

Problem 8CT

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Question

A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercise,
determine the number of diagonals for the given polygon.
B
Diagonal
D.
octagon (8 sides)

Expert Solution

Step 1

There are 8 vertices in a octagon.

We have to pick 2 vertices from 8 vertices to draw a diagonal.

We can pick 2 points from 8 points in 8C2 ways.

But notice that there will be 8 sides of the octagon included in this 8C2

We have to subtract those 8 sides.

So total number of diagonals= (8C2)-8

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