ISEE Upper Level Math : How to find an angle in other polygons
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Example Questions
Example Question #11 : How To Find An Angle In Other Polygons
The measures of the angles of a ten-sided polygon, or decagon, form an arithmetic sequence. The least of the ten degree measures is 
This polygon cannot exist.
This polygon cannot exist.
The total of the degree measures of any ten-sided polygon is
In an arithmetic sequence, the terms are separated by a common difference, which we will call 
Their sum is
The greatest of the angle measures is
However, an angle measure cannot exceed 
Example Question #21 : Isee Upper Level (Grades 9 12) Mathematics Achievement
The seven-sided polygon - or heptagon - in the above diagram is regular. What is the measure of 
In the diagram below, some other angles have been numbered for the sake of convenience.
An interior angle of a regular heptagon has measure
This is the measure of 
As a result of the Isosceles Triangle Theorem, 
This is also the measure of 
By angle addition,
Again, as a result of the Isosceles Triangle Theorem, 
Example Question #21 : Geometry
What is the sum of all the interior angles of a decagon (a polygon with ten sides)?
The sum of the angles in a polygon can be found using the equation below, in which t is equal to the total sum of the angles, and n is equal to the number of sides.
Example Question #14 : How To Find An Angle In Other Polygons
If each angle in a pentagon is equal to 
The sum of the angles in a polygon can be found using the equation below, in which t is equal to the total sum of the angles, and n is equal to the number of sides.
Given that a hexagon has 6 angles, the total number of angles will be:
To find the value of each angle, we divide 540 by 5. This results in 108 degrees.
Thus,
Example Question #15 : How To Find An Angle In Other Polygons
What is the value of an angle (to the nearest degree) in a polygon with 
The sum of the angles in a polygon can be found using the equation below, in which t is equal to the total sum of the angles, and n is equal to the number of sides.
Given that a hexagon has 6 angles, the total number of angles will be:
Given that there are 3,600 degrees total in a polygon with 22 sides, the number of degrees in each angle can be found by dividing 3,600 by 22. To the nearest degree, this results in 164 degrees. Therefore, 164 is the correct answer.
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