Define Vertical Angles

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Vertical angles are those angles which are opposite to each other when two lines cross each other. These can be better understood by the following figure:- 

 In the above figure angle 1 and 3 & angle 2 and 4 are vertical opposite angles. It is important to note that these angles are always. That is angle 1 = angle 3, and angle 2 = angle 4.
This is very important part of the geometry. One can find unknown variable especially unknown angles with this concept knowledge.

Example 1:- Find the unknown angle 1 and 3 in the below mentioned figure.  

Solution: Given One angle is 60 degree and other angle is 120 degrees.

 We have to find the value of angle 3 and angle 4.

For the same we know that vertical opposite angles are equal

 Since Angle 3 and Angle 120 degrees are vertical opposite angles, so they must be equal.

 Hence, Angle 3 = 120 degrees.

 Similarly Angle 4 and 60 degree are vertical opposite angles, so they must be equal.

 Hence, Angle 4 = 60 degrees

 In this we have evaluated two unknown angles.

Example 2:- Find the unknown angle 1 and 3 in the below mentioned figure.


Solution: Given One angle is 80 degree and other angle is 100 degrees.

 We have to find the value of angle 3 and angle 4

 For the same we know that vertical opposite angles are equal

 Since Angle 3 and Angle 100 degrees are vertical opposite angles, so they must be equal.

 Hence, Angle 3 = 100 degrees.

 Similarly Angle 4 and 80 degree are vertical opposite angles, so they must be equal.

 Hence, Angle 4 = 80 degrees.


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