The figure over is a pentagon. All of the angles detailed (except the interior one) space exterior angles to the pentagon"s interior angles.

You are watching: How many degrees does a pentagon have

What is the value of

in the number above?Explanation:

There room two an essential things for a question choose this. The very first is to understand that a polygon has actually a complete degree measure of:

, where is the variety of sides.Therefore, a hexagon favor this one has:

.Next, you must remember that all of the exterior angles listed are supplementary to your correlative inner angles. This allows you draw the complying with figure:

Now, girlfriend just have to control your algebra well. You must sum up all of the inner angles and set them equal to

. Thus, you have the right to write:Solve for

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### Example question #2 : exactly how To discover An angle In A Pentagon

The figure above is a pentagon. Every one of the angles provided (except the interior one) room exterior angle to the pentagon"s interior angles.

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

**Possible Answers:**

**Correct answer:**

Explanation:

There room two an essential things because that a question prefer this. The an initial is to recognize that a polygon has actually a full degree measure of:

, where is the variety of sides.Therefore, a hexagon favor this one has:

.Next, you should remember that every one of the exterior angles noted are supplementary to their correlative internal angles. This allows you attract the complying with figure:

Now, you just have actually to regulate your algebra well. You need to sum up every one of the interior angles and set them equal to

. Thus, you have the right to write:Solve for

:Now, you have to uncover the *largest* unknown angle, i m sorry is

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### Example question #3 : just how To find An edge In A Pentagon

What is the sum of three angles in a pentagon?

**Possible Answers:**

**Correct answer:**

Explanation:

The sum of all angles is figured out by the complying with formula because that a polygon:

In a pentagon, there are 5 sides, or

. Substitute and also find the total possible angle in a pentagon.There are 5 inner angles in a pentagon. Divide the total feasible angle by 5 to identify the value of one inner angle.

See more: Frequent Question: How Many Bonds Can Phosphorus Make ? How Many Covalent Bonds Does Phosphorus Form

Each inner angle the a pentagon is 108 degrees.

The amount of 3 angles in a pentagon is:

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