How to find an angle in a hexagon - ACT Math
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All of the angles marked are exterior angles.
What is the value of 
in degrees? Round to the nearest hundredth.
All of the angles marked are exterior angles.
What is the value of
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:
Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to 
. Since there are 
angles, you know that the numeric portion will be 
or 
. Thus, you can write:
Simplify and solve for 
:
This is 
or 
.
There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:
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:
Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to
Simplify and solve for
This is
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The sum of all the angles inside of a regular hexagon is 
. Determine the value of one angle.
The sum of all the angles inside of a regular hexagon is
In a regular hexagon, all of the sides are the same length, and all of the angles are equivalent. The problem tells us that all of the angles inside the hexagon sum to 
. To find the value of one angle, we must divide 
by 
, since there are 
angles inside of a hexagon.
In a regular hexagon, all of the sides are the same length, and all of the angles are equivalent. The problem tells us that all of the angles inside the hexagon sum to
Compare your answer with the correct one above
The figure above is a hexagon. All of the angles listed (except the interior one) are exterior angles to the hexagon's interior angles.
What is the value of 
?
The figure above is a hexagon. All of the angles listed (except the interior one) are exterior angles to the hexagon's interior angles.
What is the value of
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:
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 
:
There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:
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:
Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to
Solve for
Compare your answer with the correct one above