Question 920277

Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the two interior, opposite (remote) angles.

given triangle abc with exterior angle angle acd and the given is the measure of angle acd equals the measure of angle a plus the measure of angle b

Proof:

statement:.................................................reason:
1) &#8710;{{{ABC}}} has exterior angle <{{{ACD}}} ........- Given

2) <{{{A}}} and <{{{B}}}  are the opposite interior 
angles with respect to <{{{ACD}}}.................- Definition of opposite interior angle

3) m<{{{BCD}}} = {{{180}}}°......................- Definition of straight angle

4) m<{{{BCA}}} + <{{{ACD}}} = m<{{{BCD}}}..............- Angle addition postulate

5) m<{{{BCA}}} + m<{{{ACD}}} = {{{180}}}°...........- Substitution (3) into (4)

6) m<{{{ABC}}} + m<{{{BCA}}} + m<{{{BAC}}} = {{{180}}}°........- Sum of interior angles of a triangle

7) m<{{{BCA}}} + m<{{{ACD}}}=m<{{{ABC}}}+m<{{{BCA}}}+m<{{{BAC}}}.........Substitution (5) into (6)

8) m<{{{ACD}}} = m<{{{ABC}}} + m<{{{BAC}}}............- Subtraction property of equality