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:

Step1: Recall the definition of supplementary angles

Two angles are supplementary if their sum is \(180^{\circ}\).

Step2: Analyze the relationship between an exterior angle and its adjacent interior angle

By the definition of a linear pair (two adjacent angles that form a straight line), an exterior angle of a triangle and its adjacent interior angle form a linear pair. Since a straight line measures \(180^{\circ}\), the sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). So, an exterior angle is supplementary to the adjacent interior angle.

Step3: Analyze the other options

• For the option “An adjacent interior angle is supplementary to a remote interior angle”: There is no such general rule. The sum of two remote interior angles is equal to the exterior angle (by the exterior - angle theorem), not supplementary.
• For the option “A remote interior angle is congruent to the exterior angle”: By the exterior - angle theorem, the exterior angle is equal to the sum of the two remote interior angles, not congruent to a single remote interior angle.
• For the option “An exterior angle is supplementary to a remote interior angle”: There is no such general rule. The sum of two remote interior angles is equal to the exterior angle (by the exterior - angle theorem), not supplementary.

Answer:

An exterior angle is supplementary to the adjacent interior angle