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

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What is the worth of

in the figure above?

Explanation:

There space two vital things because that a question like this. The an initial is to understand that a polygon has actually a complete degree measure of:

, where
is the variety of sides.

Therefore, a hexagon choose this one has:

Next, you must remember that every one of the exterior angles listed are supplementary to your correlative interior angles. This lets you attract the complying with figure:

Now, girlfriend just have actually to regulate your algebra well. You should sum up every one of the internal angles and set them same to

. Thus, you can write:

Solve for

:

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

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

What is the value of the largest unknown edge in the number above?

Explanation:

There room two key things because that a question favor this. The an initial is to recognize that a polygon has a total degree measure up of:

, where
is the variety of sides.

Therefore, a hexagon prefer this one has:

.

Next, you should remember that all of the exterior angles listed are supplementary to their correlative inner angles. This lets you attract the adhering to figure:

Now, friend just have actually to regulate your algebra well. You have to sum up every one of the internal angles and collection them same to

. Thus, you have the right to write:

Solve for

:

Now, you have actually to uncover the largest unknown angle, which is

:

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

What is the amount of three angles in a pentagon?

Explanation:

The amount of all angle is figured out by the adhering to formula because that 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 feasible angle by 5 to identify the worth of one inner angle.

Each inner angle that a pentagon is 108 degrees.

The amount of 3 angles in a pentagon is:

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