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High School Math : How to find an angle in a polygon

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Example Questions

Example Question #1 : How To Find An Angle In A Polygon

What is the magnitude of the interior angle of a regular nonagon?

Possible Answers:

129^o

144^o

140^o

135^o

Correct answer:

140^o

Explanation:

The equation to calculate the magnitude of an interior angle is $\frac{180(n-2)}{n}=int\ angle$ , where is equal to the number of sides.

For our question, n=9 .

$int\ angle= \frac{180(9-2)}{9}=\frac{(180)(7)}{9}=140^o$

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Example Question #12 : Geometry

What is the interior angle measure of any regular heptagon?

Possible Answers:

125.8

135

130.2

128.6

Correct answer:

128.6

Explanation:

To find the angle of any regular polygon you find the number of sides, . In this example, n=7 .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon. 5*180=900

Then to find one individual angle we divide 900 by the total number of angles, 7.

$\frac{900}{7}=128.6$

The answer is 128.6 .

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Example Question #13 : Other Polygons

A regular polygon with sides has exterior angles that measure $1.5^{\circ }$ each. How many sides does the polygon have?

Possible Answers:

120

180

This figure cannot exist.

240

150

Correct answer:

240

Explanation:

The sum of the exterior angles of any polygon, one per vertex, is $360 ^{\circ }$ . As each angle measures $1.5^{\circ }$ , just divide 360 by 1.5 to get the number of angles.

$360 \div 1.5=240$

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Example Question #14 : Other Polygons

What is the interior angle measure of any regular nonagon?

Possible Answers:

$140^{\circ}$

$120^{\circ}$

$200^{\circ}$

$160^{\circ}$

Correct answer:

$140^{\circ}$

Explanation:

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by 180 degrees to yield a total number of degrees in the regular nonagon.

7*180=1260

Then to find one individual angle we divide 1260 by the total number of angles .

$\frac{1260}{9}=140$

The answer is 140 .

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Example Question #12 : Geometry

What is the measure of one exterior angle of a regular seventeen-sided polygon (nearest tenth of a degree)?

Possible Answers:

$34.0 ^{\circ }$

$21.2^{\circ }$

$10.6^{\circ }$

$15.9^{\circ }$

$25.2 ^{\circ }$

Correct answer:

$21.2^{\circ }$

Explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is $360^{\circ}$ . In a regular polygon, all of these angles are congruent, so divide 360 by 17 to get the measure of one exterior angle:

$360 \div 17 \approx 21.2^{\circ }$

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Example Question #13 : Geometry

What is the measure of one exterior angle of a regular twenty-three-sided polygon (nearest tenth of a degree)?

Possible Answers:

$14.4^{\circ }$

$31.3^{\circ }$

$28.8^{\circ }$

$7.8^{\circ }$

$15.7 ^{\circ }$

Correct answer:

$15.7 ^{\circ }$

Explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is $360^{\circ}$ . In a regular polygon, all of these angles are congruent, so divide 360 by 23 to get the measure of one exterior angle:

$360 \div 23 \approx 15.7 ^{\circ }$

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Example Question #4 : How To Find An Angle In A Polygon

What is the measure of one interior angle of a regular twenty-three-sided polygon (nearest tenth of a degree)?

Possible Answers:

$164.3^{\circ }$

$154.3^{\circ }$

$169.3^{\circ }$

$174.3^{\circ }$

$159.3^{\circ }$

Correct answer:

$164.3^{\circ }$

Explanation:

The measure of each interior angle of a regular polygon with sides is $\frac{180 (N-2)}{N}$ . We can substitute N = 23 to obtain the angle measure:

$\frac{180 (N-2)}{N} = \frac{180 (23-2)}{23} = \frac{180 \cdot 21}{23}\approx 164.3^{\circ }$

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Example Question #5 : How To Find An Angle In A Polygon

A regular polygon has interior angles which measure $162^{\circ }$ each. How many sides does the polygon have?

Possible Answers:

Correct answer:

Explanation:

The easiest way to answer this is to note that, since an interior angle and an exterior angle form a linear pair - and thus, a supplementary pair - each exterior angle would have measure $180-162 = 18^{\circ }$ . Since 360 divided by the number of sides of a regular polygon is equal to the measure of one of its exterior angles, we are seeking such that

$\frac{360}{N} = 18$

Solve for :

$\frac{360}{N}\cdot N= 18\cdot N$

18N = 360

$18N \div 18= 360\div 18$

N = 20

The polygon has 20 sides.

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High School Math : How to find an angle in a polygon

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find An Angle In A Polygon

Example Question #12 : Geometry

Example Question #13 : Other Polygons

Example Question #14 : Other Polygons

Example Question #12 : Geometry

Example Question #13 : Geometry

Example Question #4 : How To Find An Angle In A Polygon

Example Question #5 : How To Find An Angle In A Polygon

All High School Math Resources

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