PSAT Math : How to find an angle in a pentagon

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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

What is the measure, in degrees, of one interior angle of a regular pentagon?

Possible Answers:

180

72

108

120

144

Correct answer:

108

Explanation:

The formula for the sum of the interior angles of any regular polygon is as follows:

where  is equal to the number of sides of the regular polygon.

Therefore, the sum of the interior angles for a regular pentagon is:

To find the measure of one interior angle of a regular pentagon, simply divide by the number of sides (or number of interior angles):

The measure of one interior angle of a regular pentagon is 108 degrees.

Example Question #2 : How To Find An Angle In A Pentagon

Pentagon_1

 

Refer to the above figure, which shows Square   and regular Pentagon .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By angle addition,

 

 is one of two acute angles of isosceles right triangle , so .

 

To find  we examine .

 is an angle of a regular pentagon and has measure .

Also, since, in , sides , by the Isosceles Triangle Theorem, 

Since the angles of a triangle must total  in measure, 

 

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