GRE Math : How to find an angle in a pentagon
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Example Questions
Example Question #1 : How To Find An Angle In A Pentagon
In a five-sided polygon, one angle measures 
To find the sum of the interior angles of any polygon, use the formula 
In this case:
The sum of the interior angles will be 540. Go through each answer choice and see which one adds up to 540 (including the original angle given in the problem).
The only one that does is 120, 115, 95, 105 and the original angle of 105.
Example Question #51 : Geometry
In a particular heptagon (a seven-sided polygon) the sum of four equal interior angles, each equal to 
Quantity A:
Quantity B:
The two quantities are equal.
Quantity B is greater
The relationship cannot be determined.
Quantity A is greater.
Quantity A is greater.
The sum of interior angles in a heptagon is 
Three interior angles (call them 
Further more, all of these angles must sum up to 
We may not be able to find 
Example Question #3 : How To Find An Angle In A Pentagon
What is the value of 
Always begin working through problems like this by filling in all available information. We know that we can fill in two of the angles, giving us the following figure:
Now, we know that for any polygon, the total number of degrees in the figure can be calculated by the equation:
Thus, for our figure, we have:
Based on this, we know:
Simplifying, we get:
Solving for 
Example Question #4 : How To Find An Angle In A Pentagon
Quantity A: The measure of the largest angle in the figure above.
Quantity B:
Which of the following is true?
The relationship cannot be determined.
Quantity B is larger.
The two quantities are equal.
Quantity A is larger.
Quantity A is larger.
To begin, recall that the total degrees in any figure can be calculated by:
Now, based on our figure, we can make the equation:
Simplifying, we get:
This means that 
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