Mathematics

P: If two lines intersect then the vertically opposite angles are equal.
Q: the sum of all the angles around a point is $$180^o$$.
Then which of the following options hold?


ANSWER

P is true and Q is false


SOLUTION
Statement P is True 

Consider line $$AOB$$

$$ \angle AOD + \angle BOD  = 180^{\circ}$$  ......(1)


Now, consider line $$COD$$


$$ \angle AOC + \angle AOD = 180^{\circ}$$  ......(2)


equate both equations, we get


$$ \angle AOD + \angle BOD  = \angle AOC +\angle BOD$$


$$ \Rightarrow  \angle AOC  = \angle BOD $$  these are vertically opposite angles and are equal.


 Statement Q is False 


the sum of all angles around a Point  $$=360^{\circ}$$ 

Not $$180^{\circ}$$


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