Question

Proof:

Its is given that ∠1 and ∠2 are supplementary. ∠1 and ∠3 are also supplementary, so _______
Since ∠2 and ∠3 are corresponding angles, a║b.

A. ∠3 and ∠2 are supplementary.

B. ∠2=∠3

C. ∠2≈∠3

D. ∠2 and ∠3 are not supplementary.

Answer 1

From the figure it i obvious that angle 2 and angle 3 are equal so option C is correct.

Answer 2

Option B is correct

`\angle 2 = \angle 3`

Explanation:

Given that:

`\angle 1` and
`\angle 2` are supplementary.

prove that:
`a || b`

It is given that:

`\angle 1` and
`\angle 2` are supplementary.

By definition of supplementary

⇒
`\angle 1+ \angle 2 =180^(\circ)` .....[1]

From the figure, you can see that:

`\angle 1` and
`\angle 3` are also supplementary.

⇒
`\angle 1+ \angle 3 =180^(\circ)` .....[2]

By [1] and [2] we have;

⇒
`\angle 1+ \angle 2=\angle 1+ \angle 3`

Simplify:

`\angle 2 = \angle 3`

Since ∠2 and ∠3 are corresponding angles.

Corresponding angles states when the two lines are parallel, then Corresponding Angles are equal and vice versa.

by definition we have;

`a || b` proved!