Question

Which is a correct two-column proof? Given: <H and <X are supplementary. prove: l || n

Answer 1

Option (B) is correct

Explanation:

∠H and ∠X are supplementary as given, ∠H + ∠X = 180

And, ∠H = ∠E ( Vertical opposite angles are equal )

So, by substitution ∠E + ∠X = 180

So, the sum of same side interior angles ∠E and ∠X is 180 therefore, by using converse of same-side Interior angles theorem we get l║m.

The correct option is B

Answer 2

option-B

Explanation:

we are given

<H and <X are supplementary angles

so,

<H+<X=180

we know that

<H and <E are vertically opposite angles

so, they must be equal

<H=<E

we can plug it

<E+<X=180

It means that angle(E) and angle(X) are supplementary angles

and these two angles are same side interior angles

By using same side interior angles converse

so, line(l) and line(n) must be parallel

so, option-B