Draw intersecting lines and mark two pairs of vertically opposite angles.
Answers
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
=
2
1
∠AOC+∠AOD+
2
1
∠BOD
=
2
1
∠BOD+∠AOD+
2
1
∠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.
solution
Step-by-step explanation: