Question

Given: Line A B intersects Line D E at point C.
Prove: AngleDCB Is-congruent-toAngleECA

Line D E intersects line B A at point C.
A 2-column table with 6 rows. Column 1 is labeled statements with the entries line A B intersects line D E at point C, angle D C B and angle B C E are a linear pair, angle D C B is supplementary to angle B C E, angle B C E and angle E C A are a linear pair, angle B C E is supplementary to angle E C A, angle D C B is-congruent-to angle E C A. Column 2 is labeled reasons with the entries given, definition of linear pair, linear pair post, definition of linear pair, question mark, congruent to supplementary theorem.
What is the missing reason in step 5?

linear pair postulate
given
definition of complementary angles
congruent complements theorem

Answer 1

Linear pair postulate.

Reason: Since ∠BCE and ∠ECA form a linear pair, the linear pair postulate implies they are supplementary.