Answer:
Angles vertically opposite to each other are equal.
Step-by-step explanation:
There are two lines AB and CD intersecting at point O making angles 1 ,2,3 and 4.
The angles 1 and3 , angles 2 and 4 are vertically opposite angles.
Now consider the line AB
<1 + <2= 180 degrees--------- eq A
Now consider the line CD
<2+ <3= 180 degrees-----------eq B
As both equations are equal
< 1+ <2= <2+ <3 = 180 degrees
or
< 1+ <2= <2+ <3 or
< 1= <3 subtracting <2 from both sides
Now consider the line BA
<3+ <4= 180 degrees--------- eq C
Now consider the line DC
<4+ <1= 180 degrees-----------eq D
As both equations are equal
< 3+ <4= <4+ <1 = 180 degrees
or
< 3+ <4= <4+ <1
or
< 3= <1 subtracting <4 from both sides
This holds true for all vertically opposite angles that they are equal.
These can be measured with a protractor.
This can also be proved that if we add angles 1,2,3 and 4 we will get 360
and if we subtract angles 1 & 2 from 360 we will get 180 degrees which angles 3&4 make together.
<1+<2+<3+<4= 360 degrees
But <1 +<2= 180
360 - [ <1+<2] = 180 degrees
<3 +<4= 180
<1 +<2= <3 +<4= 180
