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Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.m_FEHFGE699HJ46°1A) 103C) 49°B) 145°D) 134

User Bryan Matthews
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1 Answer

12 votes
12 votes

ANSWER:

D) 134°

Explanation:

We have that the FEJ and GEI angles are equal, therefore:


\begin{gathered} \text{FEJ}=\text{GEI} \\ \text{FEJ}=\text{GEH}+\text{HEI} \\ \text{FEJ}=69+46 \\ \text{FEJ}=115 \end{gathered}

Now we have that the FEG and JEI angles are equal, we can calculate the value of these angles since we know that the sum of all the angles is equal to 360°, therefore:


\begin{gathered} 360=\text{FEG}+\text{JEI}+\text{FEJ}+\text{GEI} \\ \text{FEG}=\text{JEI} \\ \text{FEJ=GEI}=115 \\ 360=2\text{FEG}+115+115 \\ \text{Solving for FEG} \\ \text{FEG}=(360-230)/(2) \\ \text{FEG}=65 \end{gathered}

Now the value of FEH is equal to the sum of the FEG and GEH, we replace we have:


\begin{gathered} \text{FEH}=\text{FEG}+\text{GEH} \\ \text{FEH}=65+69 \\ \text{FEH}=134\text{\degree} \end{gathered}

Which means that the angle FEH is 134°

User Linamnt
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