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:

Analyze the relationship between adjacent interior and exterior angles

Using the Linear Pair Postulate knowledge point
An interior angle of a triangle and its adjacent exterior angle form a linear pair along a straight line, meaning they are supplementary and sum to \(180^\circ\).

Evaluate the remaining statements

Using the Exterior Angle Theorem knowledge point
An exterior angle equals the sum of the two remote interior angles, so it is not generally congruent or supplementary to a single remote interior angle.

Answer:

• (A) An exterior angle is supplementary to the adjacent interior angle. (Correct answer)
• (B) An adjacent interior angle is supplementary to a remote interior angle.
• (C) A remote interior angle is congruent to the exterior angle.
• (D) An exterior angle is supplementary to a remote interior angle.