ACT Math : How to find an angle in a pentagon

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Pentex11

The figure above is a pentagon.  All of the angles listed (except the interior one) are exterior angles to the pentagon's interior angles.

What is the value of  in the figure above?

Possible Answers:

Correct answer:

Explanation:

There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:

, where  is the number of sides.

Therefore, a hexagon like this one has:

Next, you should remember that all of the exterior angles listed are supplementary to their correlative interior angles. This lets you draw the following figure: 

Pentex12

Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to . Thus, you can write:

Solve for :

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

Pentex21

The figure above is a pentagon.  All of the angles listed (except the interior one) are exterior angles to the pentagon's interior angles.

 

What is the value of the largest unknown angle in the figure above?

Possible Answers:

Correct answer:

Explanation:

There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:

, where  is the number of sides.

Therefore, a hexagon like this one has:

.

Next, you should remember that all of the exterior angles listed are supplementary to their correlative interior angles. This lets you draw the following figure: 

 Pentex22

Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to . Thus, you can write:

Solve for :

Now, you have to find the largest unknown angle, which is :

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

What is the sum of three angles in a pentagon?

Possible Answers:

Correct answer:

Explanation:

The sum of all angles is determined by the following formula for a polygon:

In a pentagon, there are 5 sides, or .  Substitute and find the total possible angle in a pentagon.

There are 5 interior angles in a pentagon.  Divide the total possible angle by 5 to determine the value of one interior angle.

Each interior angle of a pentagon is 108 degrees.

The sum of three angles in a pentagon is:

 

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