Question

draw an opposite angle and define​

Answer 1

$\huge\pink{answer}$

Step-by-step explanation:

Draw two lines AB and CD intersecting each other at O.

We know that the vertically opposite angles are equal.

Therefore, ∠BOC=∠AOD and

∠AOC=∠BOD.

We bisect angle AOC and draw the bisecting ray as OX.

Similarly, we bisect angle BOD and draw the bisecting ray as OY.

Now, ∠XOA+∠AOD+∠DOY

=21∠AOC+∠AOD+21∠BOD

=21∠BOD+∠AOD+21∠BOD

[As, ∠AOC=∠BOD]

=∠AOD+∠BOD

Since, AB is a line.

Therefore, ∠AOD and ∠BOD are supplementary angles and the sum of these two angles will be 180°.

Therefore, ∠XOA+∠AOD+∠DOY=180°

We know that the angles on one side of a straight line will always add to 180°.

Also, the sum of the angles is 180°.

Therefore, XY is a straight line.

Thus, OX and OY are in the same line.