Plane Geometry - ACT Math
Card 0 of 2907
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?
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?
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 
:
Now, you have to find the largest unknown angle, which is 
:
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
Now, you have to find the largest unknown angle, which is
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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?
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
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
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Find the length of the diagonal for a pentagon with a a side length of 
.
Find the length of the diagonal for a pentagon with a a side length of
Use the formula for the diagonal of a pentagon:
Use the formula for the diagonal of a pentagon:
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What is the sum of three angles in a pentagon?
What is the sum of three angles in a pentagon?
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:
The sum of all angles is determined by the following formula for a polygon:
In a pentagon, there are 5 sides, or
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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Suppose the side length of a pentagon is 
. What is the area of the pentagon?
Suppose the side length of a pentagon is
Write the formula for the area of a pentagon.
Substitute the side length and simplify the radical.
Write the formula for the area of a pentagon.
Substitute the side length and simplify the radical.
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If the side of a pentagon is 
, what is the diagonal of the pentagon?
If the side of a pentagon is
Write the formula for finding the diagonal of a pentagon.
Plug in the side length and simplify.
Write the formula for finding the diagonal of a pentagon.
Plug in the side length and simplify.
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If a side of the pentagon is 
, what is the diagonal of the pentagon?
If a side of the pentagon is
Write the diagonal formula for a pentagon.
Substitute the side length and find the diagonal.
Write the diagonal formula for a pentagon.
Substitute the side length and find the diagonal.
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Find the length of the diagonal for a pentagon with a perimeter of 
.
Find the length of the diagonal for a pentagon with a perimeter of
1. Use the formula for perimeter to solve for the side length:
2. Use the formula for the diagonal of a pentagon:
1. Use the formula for perimeter to solve for the side length:
2. Use the formula for the diagonal of a pentagon:
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Find the diagonal for a pentagon with a perimeter of 
.
Find the diagonal for a pentagon with a perimeter of
1. Use the formula for perimeter to solve for the side length:
2. Use the formula for the diagonal of a pentagon:
1. Use the formula for perimeter to solve for the side length:
2. Use the formula for the diagonal of a pentagon:
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The perimeter of a regular pentagon is 
. What is the length of one side?
The perimeter of a regular pentagon is
A problem like this is very easy. A regular pentagon just looks like:
All of its sides are equal. Therefore, you know that 
, where 
is the length of one side. Solving for 
, you get 
.
A problem like this is very easy. A regular pentagon just looks like:
All of its sides are equal. Therefore, you know that
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If the perimeter of a given regular pentagon is 
. What is the length of one side of this regular pentagon in inches?
If the perimeter of a given regular pentagon is
Use the formula for perimeter to solve for the side length of the regular pentagon:
Where 
is the perimeter and 
is the length of a side.
In this case:
Use the formula for perimeter to solve for the side length of the regular pentagon:
Where
In this case:
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Find the length of each side for regular pentagon with a perimeter of 
.
Find the length of each side for regular pentagon with a perimeter of
Use the formula for perimeter to solve for the side length:
Use the formula for perimeter to solve for the side length:
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Find the length of one side for a regular pentagon with a perimeter of 
.
Find the length of one side for a regular pentagon with a perimeter of
Use the formula for perimeter to solve for the side length:
Use the formula for perimeter to solve for the side length:
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Find the length of each side for a regular pentagon with a perimeter of 
.
Find the length of each side for a regular pentagon with a perimeter of
Use the formula for perimeter to solve for the side length:
Use the formula for perimeter to solve for the side length:
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One side of a regular pentagon is 
. Find the perimeter of the pentagon.
One side of a regular pentagon is
In a regular pentagon, all of the sides are the same length.
The perimeter can then be found by summing all 
sides or multiplying 
by 
.
In a regular pentagon, all of the sides are the same length.
The perimeter can then be found by summing all
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What is the perimeter of the regular pentagon pictured above?
What is the perimeter of the regular pentagon pictured above?
The key word in this question is "regular." Since the pentagon is regular, all of its sides are equal. This means that it, in fact, looks like:
The perimeter for this is simply 
or 
.
The key word in this question is "regular." Since the pentagon is regular, all of its sides are equal. This means that it, in fact, looks like:
The perimeter for this is simply
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A regular pentagon has a side length of 
. Find its perimeter.
A regular pentagon has a side length of
Because we're told the pentagon is a regular polygon, this means that all of its sides are the same length. That is, the side lengths are congruent.
In order to solve for the perimeter, which is the sum of all sides, we can use a multiplication shortcut of:
, where 
is perimeter, 
is length of the sides, and 
is the number of sides of the polygon.
Using the information given in the problem, the values can be substituted in.
Note that this math is the same as adding 
five times:
Because we're told the pentagon is a regular polygon, this means that all of its sides are the same length. That is, the side lengths are congruent.
In order to solve for the perimeter, which is the sum of all sides, we can use a multiplication shortcut of:
Using the information given in the problem, the values can be substituted in.
Note that this math is the same as adding
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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
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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 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