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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. Download png

Tara Andrews

in Mathematics

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Kaitlin Dean on June 11, 2018

Statementscase A. ∠BEC is an exterior angleThe statement is FalseBecause, ∠BEC is an interior angle because it is located in the interior of 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 =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 in which they are supplementary angles, it is for the EBC triangle is isosceles and the segment BC is equal to the EB segmentcase E. ∠BEC is a remote interior angle 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


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