How to find an angle in a polygon - ACT Math
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In the diagram below, what is 
equal to?
In the diagram below, what is
The figure given is a hexagon with an embedded triangle. The fact that it is embedded in a triangle is mainly to throw you off, as it has little to no consequence on the correct answer. Of the available answer choices, you must choose a relationship that would give the value of 
. Tangent describes the relationship between an angle and the opposite and adjacent sides of that angle. Or in other words, tan
= opposite side/adjacent side. However, when solving for an angle, we must use the inverse function. Therefore, if we know the opposite and adjacent sides are, we can use the inverse of the tangent, or arctangent (tan-1), of 
to find 
.
Thus,
The figure given is a hexagon with an embedded triangle. The fact that it is embedded in a triangle is mainly to throw you off, as it has little to no consequence on the correct answer. Of the available answer choices, you must choose a relationship that would give the value of
Thus,
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What is the value of angle 
in the figure above?
What is the value of angle
Begin by noticing that the upper-right angle of this figure is supplementary to 
. This means that it is 
:
Now, a quadrilateral has a total of 
. This is computed by the formula 
, where 
represents the number of sides. Thus, we know:
This is the same as 
Solving for 
, we get:
Begin by noticing that the upper-right angle of this figure is supplementary to
Now, a quadrilateral has a total of
This is the same as
Solving for
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What is the angle measure for the largest unknown angle in the figure above? Round to the nearest hundredth.
What is the angle measure for the largest unknown angle in the figure above? Round to the nearest hundredth.
The total degree measure of a given figure is given by the equation 
, where 
represents the number of sides in the figure. For this figure, it is:
Therefore, we know that the sum of the angles must equal 
. This gives us the equation:
Simplifying, this is:
Now, just solve for 
:
The largest of the unknown angles is 
or 
Rounding, this is 
.
The total degree measure of a given figure is given by the equation
Therefore, we know that the sum of the angles must equal
Simplifying, this is:
Now, just solve for
The largest of the unknown angles is
Rounding, this is
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What is the interior angle of a 
polygon (a nonagon)? Round answer to the nearest hundredth if necessary.
What is the interior angle of a
To find the interior angle of an 
sided polygon, first find the total number of degrees in the polygon by the formula:
. For us that yields:
. Next we divide the total number of degrees by the number of sides:
To find the interior angle of an
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What is the total number of degrees in a 
polygon?
What is the total number of degrees in a
To find the total number of degrees in an 
-sided polygon, use the formula:
thus we see that 
To find the total number of degrees in an
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What is the interior angle of a 
polygon?
What is the interior angle of a
To find the interior angle of a regular, 
-sided polygon, use the formula:
:
Thus we see that 
and
To find the interior angle of a regular,
Thus we see that
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What is the total number of degrees in a 
polygon?
What is the total number of degrees in a
To find the total number of degrees in an 
-sided polygon, use the formula:
. Thus we see that:
To find the total number of degrees in an
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How many degrees are in the interior of an octagon (an 8-sided polygon)?
How many degrees are in the interior of an octagon (an 8-sided polygon)?
To find the total number of degrees in an 
-sided polygon, use the formula:
. Thus, for an octagon we have:
To find the total number of degrees in an
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What is the interior angle of a ten-sided polygon?
What is the interior angle of a ten-sided polygon?
To find the interior angle of an 
-sided polygon, use the equation:
Plugging in 10 for 
yields:
To find the interior angle of an
Plugging in 10 for
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What is the interior angle of a pentagon?
What is the interior angle of a pentagon?
To find the interior angle of an 
-sided polygon, use the formula:
we see for our polygon this yields:
To find the interior angle of an
we see for our polygon this yields:
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Find the total number of degrees inside a hexagon.
Find the total number of degrees inside a hexagon.
To solve, simply use the following formula where 
is the number of sides. Thus,
To solve, simply use the following formula where
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Find the total number of degrees in a heptagon.
Find the total number of degrees in a heptagon.
To solve, simply use the formula for finding the degrees in a closed polygon, given n being the number of sides.
In this particular case, a heptagon has seven sides.
Thus,
To solve, simply use the formula for finding the degrees in a closed polygon, given n being the number of sides.
In this particular case, a heptagon has seven sides.
Thus,
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