Question

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

Explanation:

• For $\triangle EBC$, $\angle BEC$ is an interior angle (not exterior), so first statement is false.
• $\angle DEC$ is outside $\triangle EBC$ and formed by extending side $EC$, so it is an exterior angle (second true).
• $\angle ABE$ and $\angle EBC$ form a linear pair on straight line $AC$, so they are supplementary (third true).
• $\angle BCF$ and $\angle DEC$: $\angle BCF$ is exterior to $\triangle EBC$, $\angle DEC$ is exterior to $\triangle EBC$; they are not supplementary (false).
• $\angle BEC$ is a remote interior angle to exterior $\angle BCF$ (since $\angle BCF = \angle BEC + \angle EBC$), so fifth true.

Answer:

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