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=(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} (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