Question

which of the following statements is true? answer m∠abd = 2(m∠cbd) m∠abc = m∠abd m∠abd = 1/2(m∠cbd) 2(m∠abd) = m∠abc

Explanation:

Step1: Recall angle - addition postulate

We know that $\angle ABC=\angle ABD + \angle CBD$. And from the figure, it seems that $\overrightarrow{BD}$ is a ray that divides $\angle ABC$ into two non - overlapping angles.

Step2: Analyze the relationship

If we assume that $\overrightarrow{BD}$ is the angle - bisector of $\angle ABC$, then $\angle ABD=\angle CBD$ and $\angle ABC = 2\angle ABD$.

Answer:

$2(\text{m}\angle ABD)=\text{m}\angle ABC$