Question

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

A. ∠BEC is an exterior angle.

B. ∠DEC is an exterior angle.

C. ∠ABE and ∠EBC are supplementary angles.

D. ∠BCF and ∠BEC are supplementary angles.

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

Answer 1

hello! the answer is B C E.

a mod keeps deleting my answer:(

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