Question

Draw a pair of intersecting
lines. Label and measure the
vertically opposite angles.​

Answer 1

Answer:

9th

Maths

Lines and Angles

Pair of Angles

Draw a pair of vertically o...

MATHS

Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

HARD

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ANSWER

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