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

General
1

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.

2

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.

Answer: To determine which statement regarding the interior and exterior angles of a triangle is always true, let’s analyze each statement individually:

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

    • This statement is true. By definition, an exterior angle of a triangle is formed by extending one side of the triangle. The exterior angle and the adjacent interior angle form a linear pair, meaning they are supplementary and their measures add up to 180^\circ.

  2. An adjacent interior angle is supplementary to a remote interior angle.

    • This statement is false. Adjacent interior angles are not supplementary to remote interior angles. Adjacent interior angles are the angles next to each other, and their sum does not necessarily equal 180^\circ.

  3. A remote interior angle is congruent to the exterior angle.

    • This statement is false. A remote interior angle is not congruent to the exterior angle. Instead, the exterior angle is equal to the sum of the two remote interior angles.

  4. An exterior angle is supplementary to a remote interior angle.

    • This statement is false. An exterior angle is not supplementary to a remote interior angle. The exterior angle is equal to the sum of the two remote interior angles.

Therefore, the correct statement that is always true is:

An exterior angle is supplementary to the adjacent interior angle.

This is because the exterior angle and the adjacent interior angle form a linear pair and their measures add up to 180^\circ.