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Please help with this! I've been struggling for a bit

Please help with this! I've been struggling for a bit-example-1
User Kayo Lima
by
8.0k points

1 Answer

4 votes

Answer:

29 degrees

Explanation:

Secants FH and LH form an angle at H and two intercepted arcs, FL and GJ.

By circle's theorem:

Therefore:


m\angle H=(1)/(2)(m\widehat{FL}-m\widehat{GJ})

Substitute the known angles:


15\degree=(1)/(2)(59\degree-m\widehat{GJ})

We solve the equation for the measure of arc GJ.


\begin{gathered} \text{ Multiply both sides by 2} \\ 15*2=59-m\widehat{GJ} \\ 30=59-m\widehat{GJ} \\ m\widehat{GJ}=59-30 \\ m\widehat{GJ}=29 \end{gathered}

The measure of arc GJ is 29 degrees.

User TheEagle
by
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