Question

please help me find BD. angle A is 30° and BC is 50°

Answer 1

We have that angle BAD is an exterior angle of the circle, then, we have the following general equation:

$\measuredangle BAD=\frac{1}{2}(\hat{BD}-\hat{BC})$

where BD and BC are the measures of their respective arc.

In this case,we have the following:

$\begin{gathered} \measuredangle BAD=30\degree \\ BC=50\degree \end{gathered}$

then, using the equation and solving for BD, we get:

$\begin{gathered} \frac{1}{2}(BD-50)=30 \\ \Rightarrow BD-50=2\cdot30=60 \\ \Rightarrow BD=60+50=110 \\ BD=110\degree \end{gathered}$

therefore, the measure of arc BD is 110 degrees