Question

Which postulate or theorem justifies that <3 is supplementary to <6?

A. Vertical angles theorem.
B. Corresponding angles postulate.
C. Alternate interior angles theorem.
D. Same-side interior angles theorem.

Answer 1

The Vertical angles theorem justifies that <3 is supplementary to <6.

Step-by-step explanation:

The theorem that justifies that <3 is supplementary to <6 is the Vertical angles theorem.

According to the Vertical angles theorem, when two lines intersect, the angles opposite each other are called vertical angles, and they are always congruent.

Since supplementary angles add up to 180 degrees, if <3 and <6 are vertical angles, then they must be congruent and their measures must add up to 180 degrees, making them supplementary.

The question about whether <3 is supplementary to <6 can be justified by a specific postulate or theorem. These options are part of the geometry concepts used to relate angles in certain configurations. Without additional context or diagrams, it's not possible to definitively say which postulate or theorem applies.

However, if <3 and <6 are on the same side of a transversal line and inside two parallel lines, the Same-side interior angles theorem would justify that they are supplementary. This theorem, also known as the consecutive interior angles theorem, states that if two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.