Question

Are the lines parallel in the fig. 5.11 ? Justify your answer.​

Answer 1

Answer:

Yes, the lines are parellel.

Here's the justification–

Angle EOA=Angle BOP --- (Vertically Opposite Angles)

Therefore, angle BOP= 105°

Angle BOP+Angle OPD=180° ---(Interior Angles)

105°+angle OPD=180°

Angle OPD=180°-105°

Therefore, angle OPD=75°

As this satisfies the interior angle theorem, we conclude that AB||CD.

This is your answer.

Hope this helps you!

Answer 2

Angle AOE + Angle EOB = 180° (Liner pairs)

So, 105° + Angle EOB = 180°

Angle EOB = 180-105

Angle EOB = 75°

Now, Angle EOB and OPD are formimg corresponding angles,

We also can see, EOB=75°= OPD

Now, we conclude that corresponding angles are equal......

And corresponding angles can only be equal if the lines are parallel.

So, the lines are parallel.

Hence, proved

Yes, the lines are parallel

HAVE A NICE DAY!!