Suppose Pentagon is regular. Each angle of a regular polygon of sides has measure

A pentagon has 5 sides, so set ; each angle of the regular hexagon has measure

Since one angle is given to be of measure , the pentagon might be regular - but without knowing more, it cannot be determined for certain. Therefore, the correct choice is "undetermined".

Area has no effect on the value of the interior angles of a pentagon. To find the sum of all angles of a pentagon, use the following formula, where is the number of sides:

There are 5 sides in a pentagon.

Divide this number by 5 to determine the value of each angle.

The perimeter in this question is irrelevant. Use the interior angle formula to determine the total sum of the angles in a hexagon.

There are six interior angles in a hexagon.

Each angle will be a sixth of the total angle.

Therefore, the sum of three angles in a hexagon is:

If one exterior angle is taken at each vertex of any polygon, and their measures are added, the sum is . Each exterior angle of a regular pentagon has the same measure, so if we let be that common measure, then

Solve for :

The statement is true.

The formula for the sum of the interior angles of a polygon is

,

where is the number of sides in the polygon

Plugging in our values, we get:

Dividing the sum of the interior angles by the number of angles in the polygon, we get the value for each interior angle:

To find the angle of any regular polygon you find the number of sides . For a pentagon, .

You then subtract 2 from the number of sides yielding 3.

Take 3 and multiply it by 180 degrees to yield the total number of degrees in the regular pentagon.

Then to find one individual angle we divide 540 by the total number of angles 5,

The answer is .

The following equation can be used to determine the measure of an interior angle of a regular polygon, where equals the number of sides.

In a pentagon, .

Now we can solve for the angle.

The measure of an interior angle of a regular polygon can be determined using the following equation, where equals the number of sides:

Use the interior angle formula to find the total sum of angles in a pentagon.

for a pentagon, so substitute this value into the equation and solve:

Divide this number by 5, since there are five interior angles.

The sum of four interior angles in a regular pentagon is:

The pentagon has 5 sides. To find the value of the interior angle of a pentagon, use the following formula to find the sum of all interior angles.

Substitute .

Divide this number by 5 to determine the value of each interior angle.

Every interior angle is 108 degrees. The problem states that an interior angle is . Set these two values equal to each other and solve for .