<u>Statements</u>
<u>case A</u>. ∠BEC is an exterior angle
The statement is False
Because, ∠BEC is an interior angle as it was located inside the triangle.
<u>case B.</u> ∠DEC is an exterior angle
The statement is True
<u>case C.</u> ∠ABE and ∠EBC are supplementary angles.
The statement is True
Because
∠ABE+∠EBC =
<u>case D.</u> ∠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
<u>case E.</u> ∠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