Q:

# 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.

Accepted Solution

A:
Statementscase A. ∠BEC is an exterior angleThe statement is FalseBecause, ∠BEC is an interior angle as it was located inside the triangle.case B. ∠DEC is an exterior angleThe statement is Truecase C. ∠ABE and ∠EBC are supplementary angles.The statement is TrueBecause∠ABE+∠EBC =$$180\°$$case D. ∠BCF and ∠BEC are supplementary angles.The statement is FalseBecause we know that In a triangle, each exterior angle has two remote interior angles∠BCF=∠BEC+∠EBCAdds ∠BEC both sides∠BCF+∠BEC=∠BEC+∠EBC+∠BEC(∠BCF+∠BEC)=2∠BEC+∠EBCthe only way they are supplementary angles is for the EBC triangle to be isosceles and the BC segment to be equal to the EB segmentcase E. ∠BEC is a remote interior angle to exterior ∠BCFThe statement is True    Becausewe know that In a triangle, each exterior angle has two remote interior angles∠BCF=∠BEC+∠EBCsoThe exterior angle ∠BCF has the remote interior angle ∠BEC and the remote interior angle ∠EBC