Question

which statement regarding the interior and exterior angles of a triangle is always true?
○ an exterior angle is supplementary to the adjacent interior angle.
○ an adjacent interior angle is supplementary to a remote interior angle.
○ a remote interior angle is congruent to the exterior angle.
○ an exterior angle is supplementary to a remote interior angle.

Explanation:

1. Recall the definition of supplementary angles (sum to \(180^\circ\)) and the relationship between exterior and interior angles of a triangle:

• An exterior angle of a triangle and its adjacent interior angle form a linear pair. A linear pair of angles is supplementary (their sum is \(180^\circ\)).
• For the other options:
• Adjacent interior and remote interior angles are not supplementary (their sum is equal to the exterior angle, not \(180^\circ\) in general).
• A remote interior angle is not congruent to the exterior angle (the exterior angle is equal to the sum of the two remote interior angles, so it's only congruent if the two remote angles sum to it, which isn't a general congruence).
• An exterior angle and a remote interior angle are not supplementary (their sum is more than \(180^\circ\) in most cases, as the exterior angle is sum of two remotes).

1. So the correct statement is that an exterior angle is supplementary to the adjacent interior angle.

Answer:

A. An exterior angle is supplementary to the adjacent interior angle.