Question

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are -

(1) Neither equal nor supplementary.

(2) Not equal but supplementary.

(3) Equal but not supplementary.

(4) Either equal or supplementary.​

Answer 1

Answer:

Correct option is

D

either equal or supplementary

Step-by-step explanation:

Given that, Arms of one angle are parallel to arms of another angle.

It is obvious that, if corresponding sides are parallel, then their corresponding angles are also equal.

Now, take the example of following figure:

Here, ∠ABC is one angle ∠DCB is another angle. Where AB arm is parallel to CD. Both the base arms coincided.

Now, as AB is parallel to CD and BC is the transversal, α=γ(∵alternative angles)...eq.1

And β+γ=180  

o

(∵straight angle)

⇒β+α=180  

o

(from eq.1)  

Hence, both the angles will be either equal or supplementary ( i.e. sum go angles being 180  

o

 )