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

Find m,c show all the calculations that lead to the final answer-example-1
User Alex Hirzel
by
3.3k points

1 Answer

26 votes
26 votes

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

Therefore, angle C measures 18°.

User Rymanso
by
3.2k points
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