Question

Which statements regarding the diagram of ΔEBC are true? Check all that apply.

Answer 1

The answer would be:
B. ∠DEC is an exterior angle.
C. ∠ABE and ∠EBC are supplementary angles.

∠BEC is an interior angle as it was located inside the triangle. ∠DEC is an exterior angle since it was located outside the triangle. ∠ABE and ∠EBC are supplementary angles because their sum is 180. ∠BCF is not making a supplementary angle with ∠BEC.
∠BEC and ∠EBC is a remote interior angle to exterior ∠BCF. I think it should be false since the option only put one of the remote interior angles.

Answer 2

Statements

case A. ∠BEC is an exterior angle

The statement is False

Because, ∠BEC is an interior angle as it was located inside the triangle.

case B. ∠DEC is an exterior angle

The statement is True

case C. ∠ABE and ∠EBC are supplementary angles.

The statement is True

Because

∠ABE+∠EBC =$180\°$

case D. ∠BCF and ∠BEC are supplementary angles.

The statement is False

Because

we know that

In a triangle, each exterior angle has two remote interior angles

∠BCF=∠BEC+∠EBC

Adds ∠BEC both sides

∠BCF+∠BEC=∠BEC+∠EBC+∠BEC

(∠BCF+∠BEC)=2∠BEC+∠EBC

the only way they are supplementary angles is for the EBC triangle to be isosceles and the BC segment to be equal to the EB segment

case E. ∠BEC is a remote interior angle to exterior ∠BCF

The statement is True    

Because

we know that

In a triangle, each exterior angle has two remote interior angles

∠BCF=∠BEC+∠EBC

so

The exterior angle ∠BCF has the remote interior angle ∠BEC and the remote interior angle ∠EBC