Question

m\widehat{ebd}

Explanation:

Step1: Sum of arcs in a circle

The sum of all arcs in a circle is \(360^{\circ}\). But we can also calculate \(m\overarc{EBD}\) by adding the arcs \(m\overarc{EB}+m\overarc{BD}\).

Step2: Calculate \(m\overarc{EB}\) and \(m\overarc{BD}\)

We know \(m\overarc{EB} = 150^{\circ}\) and \(m\overarc{BD}=30^{\circ}\) (given in the circle diagram).

Step3: Add the arcs

\(m\overarc{EBD}=m\overarc{EB}+m\overarc{BD}\)
\(m\overarc{EBD}=150^{\circ}+30^{\circ}\)
\(m\overarc{EBD}=180^{\circ}\)

Answer:

\(180^{\circ}\)