Question

which statements regarding the diagram of \\( \triangle ebc \\) are true? select three options. \\( \angle bec \\) is an exterior angle. \\( \angle dec \\) is an exterior angle. \\( \angle abe \\) and \\( \angle ebc \\) are supplementary angles. \\( \angle bcf \\) and \\( \angle dec \\) are supplementary angles. \\( \angle bec \\) is a remote interior angle to exterior \\( \angle bcf \\).

Explanation:

• An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. $\angle DEC$ is formed by side $EC$ of $\triangle EBC$ and the extension of side $ED$ (since $D - E - C$ with $D$ being an extension). So, $\angle DEC$ is an exterior angle.
• Supplementary angles are two angles that add up to $180^{\circ}$. $\angle ABE$ and $\angle EBC$ form a linear pair (they are adjacent and their non - common sides form a straight line), so $\angle ABE+\angle EBC = 180^{\circ}$, and they are supplementary.
• For an exterior angle of a triangle (e.g., $\angle BCF$), the remote interior angles are the two non - adjacent interior angles. $\angle BEC$ is a non - adjacent interior angle to the exterior angle $\angle BCF$.

• $\angle BEC$ is an interior angle of $\triangle EBC$, not an exterior angle.
• $\angle BCF$ and $\angle DEC$ are not supplementary.

Answer:

$\angle DEC$ is an exterior angle. ; $\angle ABE$ and $\angle EBC$ are supplementary angles. ; $\angle BEC$ is a remote interior angle to exterior $\angle BCF$.