All PSAT Math Resources
Example Question #1 : Pentagons
What is the measure, in degrees, of one interior angle of a regular pentagon?
The formula for the sum of the interior angles of any regular polygon is as follows:
where is equal to the number of sides of the regular polygon.
Therefore, the sum of the interior angles for a regular pentagon is:
To find the measure of one interior angle of a regular pentagon, simply divide by the number of sides (or number of interior angles):
The measure of one interior angle of a regular pentagon is 108 degrees.
Example Question #2 : Pentagons
Refer to the above figure, which shows Square and regular Pentagon .
By angle addition,
is one of two acute angles of isosceles right triangle , so .
To find we examine .
is an angle of a regular pentagon and has measure .
Also, since, in , sides , by the Isosceles Triangle Theorem, .
Since the angles of a triangle must total in measure,