Justification for each step in the geometric proofs

Question

1. Angle ABX is congruent to XBC
2. the measure of angle ABX is congruent to the measure of angle XBC
3. the measure of XBC=45 degrees
4. the measure of ABX=45 degrees
5. the measure of angle ABX plus the measure of XBC= the measure of ABC
6. 45 degrees plus 45 degrees= the measure of ABC
7. 90 degrees= the measure of ABC
8. ABC is a right angle

 

A    X

l    /

l   /

l  /

l /

B-------C

Answer 1

I drew my own diagram, which matches your statements. 

1. Given

2. Your second statement should read "equals the measure of" - not "congruent to"    Then the reason follows:

If two angles are congruent, then they have equal measure.

3. Given

4. Given

5. Angle Addition Property

6. Substitution Property

7. Arithmetic Addition

8. Definition of a right angle