Question

Given: ΔABC

Answer 1

When proving that all three angles of Triangle ABC add up to 180 degrees. The flow chart is missing a reason underneath Substitution. The numbered blank space answer would be supplementary angles because they equal 180 degrees. See attached diagram for more information. The possible answers are:

Definition of Supplementary Angles (CORRECT)

Substitution (incorrect)

Definition of Complementary Angles (equal 90 degrees so Incorrect)

Angle Addition Postulate (incorrect)

Answer 2

 By Alternate Interior Angles, angle EBC is congruent to angle BCA. By Substitution, the sum of the measures of angles BCA, CBA, and BAC equals 180 degrees. Next path, by Construction, line segment DE is parallel to line segment AC. By Alternate Interior Angles, angle DBA is congruent to angle BAC. By Substitution, the sum of the measures of angles BCA, BCA, and BAC equals 180 degrees. Next path, by Construction, line segment DE is parallel to line segment AC. By Definition of a Straight Angle, the measure of angle EBD equals 180 degrees. By Substitution, the sum of the measures of angles EBC, CBA, and DBA equals 180 degrees.