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Chapter 3: Q37. (page 115)

If the measures of each interior angle of a regular polygon is 108, then the polygon is a(n)_?_.

Short Answer

Expert verified

If the measures of each interior angle of a regular polygon is 108, then the polygon ispentagon.

Step by step solution

01

Step 1. Find the formula that can be used to calculate the interior angle of a regular polygon.

The interior angle of a regular polygon with n sides is 180n−2n.

02

Step 2. Calculate the number of sides (n) by using the formula.

Equate the formula with the given information,

180n−2n=108180n−360=108n180n−108n=36072n=360n=36072=5

03

Step 3. to find the type of polygon determined by n number of sides.

The number of sides n=5. Therefore, the polygon is a pentagon.

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Most popular questions from this chapter

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

art

and

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

and

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

and

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.

e.

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

Two lines in the plane of the floor are _?_skew.
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