Question

If two lines intersect each other, then show that the vertically opposite angles are equal.​

Answer 1

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

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Answer 2

Answer:

here is the answer.

Explanation:

In the above statement it is given that "Two lines intersect with each other".

So,let AB and CD be two lines intersecting at O they lead to two pairs of vertically opposite angles namely,

(i)Angle AOC and BOD

(ii)Angle AOD and BOC

We need to prove that Angle AOC=BOD and Angle AOD=BOC

Now,ray OA stands on line CD

Therefore,Angle AOC+AOD=180°

(linear pair axiom)----(1)

Can we write, Angle AOD+BOD=180°?

(linear pair axiom)--------(2)

From eq (1) & (2) , we can write

Angle AOC + Angle AOD = Angle AOD +a

Angle BOD

This implies that

Angle AOC=Angle BOD

Similarly it can be proved that

Angle AOD = Angle BOC .

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