Question

which of the following statements is true? answer attempt 1 out of 3 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 property

We know that $\angle ABC=\angle ABD + \angle CBD$.

Step2: Analyze each option

• Option 1: $\text{m}\angle ABD = 2(\text{m}\angle CBD)$ has no basis from the given figure.
• Option 2: $\text{m}\angle ABC=\text{m}\angle ABD$ is incorrect since $\angle ABC$ is the sum of $\angle ABD$ and $\angle CBD$.
• Option 3: $\text{m}\angle ABD=\frac{1}{2}(\text{m}\angle CBD)$ has no basis from the given figure.
• Option 4: Since $\angle ABC=\angle ABD+\angle CBD$ and if we assume $\angle CBD=\angle ABD$ (from the visual appearance of the angle - bisector like situation where $BD$ seems to bisect $\angle ABC$), then $2(\text{m}\angle ABD)=\text{m}\angle ABC$.

Answer:

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