Question

Find m,c show all the calculations that lead to the final answer

Answer 1

First, we have to find the length of arc AE, knowing that the arc BDA = 180°.

$\begin{gathered} arc(AE)=180-arc(BD)-arc(DE)=180-20-104 \\ \text{arc(AE)}=56 \end{gathered}$

Then, we use the theorem about the angle formed by two secants, which is equivalent to the semi-sum of the difference between its subtended arcs.

$\begin{gathered} m\angle C=\frac{1}{2}(AE-BD)=\frac{1}{2}\cdot(56-20) \\ m\angle C=\frac{1}{2}\cdot36=18 \end{gathered}$

Therefore, angle C measures 18°.