Question

When two parallel lines are cut by a transversal, which angle pairs are supplementary?

alternate exterior angles

alternate interior angles

same side interior angles

corresponding angles

Answer 1

option C

Explanation:

correct answer is option C

Angles are given in the diagram attached below.

alternate interior angles are ∠1 and ∠3 , ∠2 and ∠4 and they are equal to each other.

alternate exterior angles are ∠1 and ∠8 , ∠2 and ∠7 they are equal to each other.

corresponding angles are ∠1 and ∠5 , ∠2 and ∠6 they are equal to each other.

where as same side interior angles are supplementary means

∠4 + ∠5 = 180°

Answer 2

The correct option is same side interior angles.

We know that when the two angles sums to 180 degrees then the angles are supplementary to each other.

Let us suppose x and y are supplementary to each other. Then we have

`x+y =1 80`

Now, we know that when two parallel lines are cut by a transversal, then consecutive interior angles adds up to 180 degrees.

Hence, same side interior angles pairs are supplementary.

C is the correct option.