Question

Statements Reasons

Answer 1

Answer:  see proof below

Step-by-step explanation:

Given: BC bisects ∠ABD

           ∠ABD = 52°

Prove: ∠ABC = 26°

$\begin{array}{l|l}\underline{\qquad\text{Statement}\qquad}&\underline{\qquad\text{Reason}\qquad}\\1.\ \angle ABD=52^o &1.\ \text{Given}\\2.\ \overline{BC}\ \text{bisects}\ \angle ABD}&2.\ \text{Given}\\3.\ \angle ABC=\angle CBD&3.\ \text{De finition of Angle Bisector}\\4.\ \angle ABC+\angle CBD=\angle ABD&4.\ \text{Angle Sum Theorem}\\5.\ \angle ABC+\angle CBD=52^o&5.\ \text{Transitive Property (S1 and S4)}\\6.\ \angle ABC+\angle ABC=52^o&6.\ \text{Substitution (S3)}\\\end{array}$

$\begin{array}{l|l}7.\ \angle ABC=26^o\qquad \quad \qquad \quad &7.\ \text{Division Property}\end{array}$