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

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Example Questions

Example Question #1 : Pentagons

What is the interior angle measure of any regular pentagon?

Possible Answers:

108

Correct answer:

108

Explanation:

To find the angle of any regular polygon you find the number of sides . For a pentagon, n=5 .

You then subtract 2 from the number of sides yielding 3.

Take 3 and multiply it by 180 degrees to yield the total number of degrees in the regular pentagon. 3*180=540

Then to find one individual angle we divide 540 by the total number of angles 5, $\frac{540}{5}=108$

The answer is 108 .

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

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

Possible Answers:

108^o

180^o

120^o

90^o

Correct answer:

108^o

Explanation:

The following equation can be used to determine the measure of an interior angle of a regular polygon, where $\small n$ equals the number of sides.

$\angle=\frac{180(n-2)}{n}$

In a pentagon, $\small n=5$ .

$\angle=\frac{180(5-2)}{5}$

Now we can solve for the angle.

$\angle=\frac{180(3)}{5}=\frac{540}{5}=108^o$

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

Find the interior angle of the following regular pentagon:

Angle_length_of_side_pentagon

Possible Answers:

$114^{\circ}$

$108^{\circ}$

$110^{\circ}$

$112^{\circ}$

$116^{\circ}$

Correct answer:

$108^{\circ}$

Explanation:

The formula for the sum of the interior angles of a polygon is

$X=(s-2)(180^{\circ})$ ,

where is the number of sides in the polygon

Plugging in our values, we get:

$X=(5-2)(180^{\circ})$

$X=540^{\circ}$

Dividing the sum of the interior angles by the number of angles in the polygon, we get the value for each interior angle:

$\frac{X}{5}=\frac{540^{\circ}}{5}=108^{\circ}$

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

What is the measure of an interior angle of a regular pentagon?

Possible Answers:

108

120

Correct answer:

108

Explanation:

The measure of an interior angle of a regular polygon can be determined using the following equation, where equals the number of sides:

$\angle=\frac{180(n-2)}{n}$

$\angle=\frac{180(5-2)}{5}=\frac{180(3)}{5}=108$

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

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Pentagons

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

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

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

All High School Math Resources

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