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# Polygons, Five Sides and Up Help (page 2)

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By — McGraw-Hill Professional
Updated on Oct 3, 2011

## Polygons, Five Sides and Up Practice Problems

#### PROBLEM 1

What is the measure of each interior angle of a regular hexagon?

#### SOLUTION 1

Draw a horizontal line segment to start. All the other sides must be duplicates of this one, but rotated with respect to the first line segment by whole-number multiples of a certain angle. This rotation angle from side to side is 360° divided by 6 (a full rotation divided by the number of sides), or 60°. Imagine the lines on which two adjacent sides lie. Look back at Fig. 4-2. These lines subtend a 60° angle with respect to each other, if you look at the acute angle. But if you look at the obtuse angle, it is 120°. This obtuse angle is an interior angle of the hexagon. Therefore, each interior angle of a regular hexagon measures 120°.

Fig. 4-2 . A regular hexagon. Each side is s units long, and each interior angle has measure z . The extensions of sides (dashed lines) are the subject of Problem 1.

#### PROBLEM 2

Briefly glance at the lowermost polygon in Fig. 4-4 (the one with the shaded interior). Don’t look at it for more than two seconds. How many sides do you suppose this object has?

Fig. 4-4 . General, many-sided polygons. The object with the shaded interior is the subject of Problem 2.

#### SOLUTION 2

This is an optical illusion. Most people underestimate the number of sides in figures like this. After you’ve made your guess, count them and see for yourself!

Practice problems for these concepts can be found at: Other Plane Figures Practice Test.

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