Given that:
[tex]AB\perp BD[/tex]And given that these angles are Complementary (they add up to 90 degrees):
[tex]\begin{gathered} \angle EFG \\ \angle ABC \end{gathered}[/tex]22. A Right Angle is an angle that measures 90 degrees. Therefore, by the definition of Right Angles:
[tex]\angle ABD=90°[/tex]23. According to the Angle Addition Postulate, if two or more angles are next to each other and have a common vertex, then the total measure of the angle is obtained by adding them.
Therefore, in this case:
[tex]m\angle ABC+m\angle CBD=m\angle ABD[/tex]24. The Substitution Property of Equality states that, if:
[tex]a=b[/tex]And:
[tex]a=c[/tex]Then:
[tex]b=c[/tex]Applying that property, you can set up that:
[tex]m\angle ABC+m\angle CBD=90\text{\degree}[/tex]25. By definition, Complementary Angles add up to 90 degrees.
Knowing that angles EFG and ABC are Complementary, you know that:
[tex]\angle EFG+\angle CBD=90°[/tex]26. The Transitive Property of Equality states that if:
[tex]a=b[/tex]And:
[tex]b=c[/tex]Then:
[tex]a=c[/tex]Therefore:
[tex]\angle ABC+\angle CBD=\angle EFG+\angle CBD[/tex]27. According to the Congruent Complements Theorem, two angles have the same measure of they are complementary to the same angles. In this case:
[tex]\angle ABC=\angle EFG[/tex]28. By definition, if two angles are congruent, they have the same measure.
Hence, the answer is.
22. Definition of Right Angles.
23.
[tex]m\angle ABC+m\angle CBD=m\angle ABD[/tex]24. Substitution Property of Equality.
25. Definition of Complementary Angles.
26 Transitive Property of Equality.
27. Congruent Complements Theorem.
28. Congruence Definition.
