ANSWER
EXPLANATION
We want to find the measure of We are given that:
[tex]\begin{gathered} <\text{BAC}=17\degree \\ <\text{BDC}=52\degree \end{gathered}[/tex]
Triangle BDC is an isosceles triangle. This means that:
[tex]<\text{BDC}=<\text{BCD}[/tex]
We need to find the measure of apply the sum of angles in a triangle:
[tex]\begin{gathered} <\text{BDC}+<\text{BCD}+<\text{CBD}=180 \\ \Rightarrow52+52+<\text{CBD}=180 \\ 104+<\text{CBD}=180 \\ \Rightarrow<\text{CBD}=180-104 \\ <\text{CBD}=76\degree \end{gathered}[/tex]
From the figure, we see that triangle ABC and ABD are congruent triangles. This means that all three sets of angles in the triangles are congruent (equal in measure).
Therefore:
[tex]<\text{ABC}=<\text{ABD}[/tex]
The sum of angles at a point is equal to 360 degrees. This means that:
[tex]<\text{ABC}+<\text{ABD}+<\text{CBD}=180[/tex]
Since angles [tex]undefined[/tex]
