Question

Given angle 1 and angle 2 are supplementary. Prove p is parallel to q.

Answer 1

It is true and proved that p║q using the corresponding angle theorem.

What are supplementary angles.

Supplementary angles are angles that complement themselves to make 180 degrees, it means that the addition of these two angles results into 180 degrees.

If there are two parallel line p and q, cut by a transversal line r. Then the alternate exterior angle ∠1 and interior angle ∠3 are equal using the corresponding angle theorem.

Also, ∠1 and ∠2 are supplementary angles if the sum of angle ∠3 and ∠2 = 180 degrees. Thus, the sum ∠1 and ∠4(opposite exterior angle on line p) is equal to the sum of ∠3 and ∠2 on line q.

Then it is proved that p║q.

Answer 2

Explanation:

We have that angle 1 and angle 2 are supplementary, thanks to the theorem that states that 2 adjacent angles whose exterior rays form a line are supplementary.

From the above we can determine that angles 2 and 3 are equal. (consecutive interior angles). Due to the above, angles 1 and 3 are equal, by transitive property.

We also have to angle 1 = angle 3 (corresponding angles).

If 2 lines are cut by a transversal so that corresponding angles are congruent (angle 1 and angle 3), then the lines are parallel (corresponding converse theorem).