What is the measure of angle ∠NOP in Fig.? Class 7

What is the measure of angle ∠NOP in Fig.? Class 7

Question 1.

What is the measure of angle ∠NOP in Fig.? Class 7

[Hint: Draw lines parallel to LM and PQ through points N and O.]

Solution:

Draw AN parallel to ML and OB parallel to QP.

Clearly, ML, NA, OB and PQ are parallel to each other.

Now, ∠MNA = ∠LMN = 40° (Alternate angles)

So, ∠ANO = 96° - 40° = 56° .......(i)

Also, ∠BOP = ∠QPO = 52° (Alternate angles)

So, a° = 56° + 52° = 108°.

Question 2.

There do not seem to be any parallel lines here. Or, are there?

What causes these illusions?

Solution:

Yes, there are parallel lines in the given figures.

Causes of these illusions are :

1. Existence of so many intersecting lines gives the impression that there are no parallel lines.
2. Movements of eyes is not able to decide about parallel lines because there is very little difference between the lines, etc.
3. Try to find out some more causes yourself.