Polygons is a geometrical figure that has many sides. There is only one important thing you should remember about Polygons. That is the sum of interior angles of a polygon.
Sum of interior angles of a polygon with " 
" sides = 
.
" sides = .
The following table summarizes the sum of interior angles for different types of polygons
Shape
|
Number of Sides
|
Sum of Interior Angles
|
Value of Each Angle if Regular Polygon
|
Triangle
 |
3
|
180
|
3 = 60
|
Quadrilateral
 |
4
|
360
|
4=90
|
Pentagon
 |
5
|
540
|
5=108
|
Hexagon
 |
6
|
720
|
6=120
|
Polygon with n sides
| | |  |
Polygons are primarily classified by the number of sides, for example a triangle is a polygon with 3 sides. Other familiar geometrical figures, such as rectangles, quadrilaterals, parallelograms are also Polygons by definition. Therefore do not be surprised if a test question refers to a rectangle as a polygon with 4-sides.
Example:
The above figure shows 
where 
= 
. If the line 
shown in the figure is parallel to , what is the value of 
?
where = . If the line shown in the figure is parallel to , what is the value of ?
A) 30º
B) 45º
C) 60º
D) 75º
E) 90º
Solution:
Step 1: In this problem, we know that line is parallel to . Since alternate angles are equal, 
should also equal 90º
is parallel to . Since alternate angles are equal, should also equal 90º
Step 2: This makes a right isosceles triangle since = . This implies that 
a right isosceles triangle since = . This implies that
The correct answer is B
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