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 =[tex]180\°[/tex]
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
