Question

1. is ∠c the same as ∠cbd? 14. how many angles in the diagram have (overrightarrow{db}) as one of their sides? list them. 15. how do you know ∠dab and ∠abd are not the same angle? explain. 16. name the vertex of ∠1. 17. name the sides of ∠4. 18. what is another name for ∠3? what is another name for ∠cad?

Explanation:

Step1: Identify angles with side $\overrightarrow{DB}$

Check all angles in the first - given diagram.
Angles $\angle ADB$, $\angle CDB$, $\angle ABD$, $\angle CBD$ have $\overrightarrow{DB}$ as one of their sides. So there are 4 such angles.

Step2: Explain $\angle DAB$ and $\angle ABD$ difference

The vertex of $\angle DAB$ is $A$, and the rays are $\overrightarrow{AD}$ and $\overrightarrow{AB}$. The vertex of $\angle ABD$ is $B$, and the rays are $\overrightarrow{BA}$ and $\overrightarrow{BD}$. Since their vertices are different, they are not the same angle.

Step3: Name vertex of $\angle1$

In the second - given diagram, the vertex of $\angle1$ is $A$.

Step4: Name sides of $\angle4$

The sides of $\angle4$ in the second - given diagram are $\overrightarrow{CA}$ and $\overrightarrow{CD}$.

Step5: Find another name for $\angle3$

Another name for $\angle3$ in the second - given diagram is $\angle ADC$.

Step6: Find another name for $\angle CAD$

Another name for $\angle CAD$ in the second - given diagram is $\angle1$.

Answer:

1. 4 angles; $\angle ADB$, $\angle CDB$, $\angle ABD$, $\angle CBD$
2. Their vertices are different. The vertex of $\angle DAB$ is $A$ and the vertex of $\angle ABD$ is $B$.
3. $A$
4. $\overrightarrow{CA}$ and $\overrightarrow{CD}$
5. $\angle ADC$
6. $\angle1$