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Chapter 3: Q17 (page 105)

The measure of each interior angle of a regular polygon is eleven times that of an exterior angle. How many sides does the polygon have?

Short Answer

Expert verified

The polygon has 12 sides.

Step by step solution

01

Step 1. Write the formula to find the measure of each interior angle of the regular polygon.

The formula to find the measure of each interior angle of the regular polygon with sides is n-2180n.

02

Step 2. Write the formula to find the measure of each exterior angle of the regular polygon.

The formula to find the measure of each exterior angle of the regular polygon with sides is 360n.

03

Step 3. Find the equation for the given statement.

Consider the number of sides of the polygon be n.

As, the measure of each interior angle of a regular polygon is elven times that of an exterior angle.

Therefore, the equation for the given statement is:

measureofeachinteriorangle=11脳measureofeachexterioranglen鈭�2180n=11脳360n

04

Step 4. Find the value of n.

Solve the above equation to find the value of n.

n鈭�2180n=11脳360nn鈭�2180=11脳360n鈭�2=11脳360180n鈭�2=11脳2n鈭�2=22n=22+2n=24

Therefore, the value of n is 24.

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Most popular questions from this chapter

Classify each pair of angles as alternate interior, same side interior or corresponding angles

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and

Name the two lines and the transversal that form each pair of angles.

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Complete each statement with the word always, sometimes, or never.

Two lines that are not coplanar intersect.

Find the values of xand y

The blue line is a transversal.

a. Name four pairs of corresponding angles.

b. Name two pairs of alternate interior angles.

c. Name two pairs of same-side interior angles.

d. Name two pairs of angles that could be called alternate exterior angles.

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