Question

use the figure below to select the true statement.$angle bec$ is an exterior angle.$angle dec$ is an exterior angle.$angle bcf$ and $angle dec$ are supplementary angles.$angle eba$ is a remote interior angle to exterior $angle bce$.

Explanation:

1. Analyze ∠BEC: This angle is inside triangle BEC, so it is an interior angle, not exterior.
2. Analyze ∠DEC: This angle is formed outside triangle BEC by extending side EC, so it is an exterior angle of the triangle.
3. Analyze ∠BCF and ∠DEC: ∠BCF is an exterior angle at C, and ∠DEC is an exterior angle at E. They are not adjacent on a straight line, so their sum is not 180°, meaning they are not supplementary.
4. Analyze ∠EBA and ∠BCE: ∠BCE is an interior angle of triangle BEC, not an exterior angle, so ∠EBA cannot be its remote interior angle.

Answer:

∠DEC is an exterior angle.