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6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Chapter A.5, Problem 35E

Textbook Problem

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*In Exercises 35 and 36, use Theorem 2.5.1 to solve the problem. According to this theorem, the number of diagonals in a polygon of n sides is given by *

Find the number of sides in a polygon that has 9 diagonals

To determine

**To find:**

To find the number of sides in a polygon that has 9 diagonals.

Consider the polygon has 9 diagonals.

**Theorem:**

If the number of diagonals in a polygon of *n* sides is given by

Where *n* is number of sides of the polygon.

Given that

Substitute the value of

Then multiply by 2 on both sides of the equation to get the following,

Subtract 18 on both sides to get the following,

The general form of the quadratic equation is given below,

Where *a* is the number multiplied by *b* is the number multiplied by *x*, and *c* is the constant term.

**Quadratic formula:**

The solution for

Compare the given equation with general equation to get the following,

Therefore,

Elementary Geometry for College Students

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