Question

To prove:the opposite angles formed by two intersecting lines are of equal measures​

Answer 1

Answer:

A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=45 °, then its opposite angle is also equal to 45 °.

Step-by-step explanation:

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Answer 2

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Answer --

We know other two angles are called a pair of vertically opposite angles if their arms form two pairs of opposite rays .

So To

Prove - Opposite angles formed by two intersecting lines are equal .

I. e. Angle AOC = Angle COD

( See The Attachement also )

Proof -

Here ray OC stands on line AB .

∠AOC + ∠BOD = 180° ( Linear Pair )-- ( i)

Again ray OB stands on line CD

So ∠BOD + ∠BOC =180 ( Linear Pair )--- (ii )

So from equation i and equation ii

∠AOC + ∠BOD = ∠BOD + ∠BOC

On subtracting ∠BOC from both sides , we get

∠AOC= ∠BOD

This Proves that the opposite angles formed by two intersecting lines are always equal.

Similarly we can also prove ∠AOD and ∠BOC by this above theorem.

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