Definition of vertical angles

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Definition of vertical angles is very important to understand in geometry. These are basically those angles which are on other extreme with respect to other angle, like a and b and c and d, it is only when the two lines cross each other. These can be better understood by the following figure:



In the above figure angle a and b & angle c and d are vertical opposite angles. It is important to note that these angles are always.
That is angle a = angle b, and angle c= angle d.


Problem 1: Find the unknown angle c and d 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 c and angle d.
=> For the same we know that vertical opposite angles are equal
=> Since Angle c and Angle 100 degrees are vertical opposite angles, so they must be equal.
=> Hence, Angle c = 100 degrees.
=> Similarly Angle d and 80 degree are vertical opposite angles, so they must be equal.
=> Hence, Angle d = 80 degrees

                                                                                                                                       
Problem 2: Find the unknown angle c and d in the below mentioned figure:-   


Solution: Given One angle is 90 degree and other angle is also 90 degrees.
=> We have to find the value of angle c and angle d
=> For the same we know that vertical opposite angles are equal
=> Since Angle c and Angle 90 degrees are vertical opposite angles, so they must be equal.
=> Hence, Angle c = 90 degrees.
=> Similarly Angle d and 90 degree are vertical opposite angles, so they must be equal.
=> Hence, Angle d = 90 degrees
=> So, all angles are equal to 90 degrees.

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