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:
[tex]m\angle H=\frac{1}{2}(m\widehat{FL}-m\widehat{GJ})[/tex]
Substitute the known angles:
[tex]15\degree=\frac{1}{2}(59\degree-m\widehat{GJ})[/tex]
We solve the equation for the measure of arc GJ.
[tex]\begin{gathered} \text{ Multiply both sides by 2} \\ 15\times2=59-m\widehat{GJ} \\ 30=59-m\widehat{GJ} \\ m\widehat{GJ}=59-30 \\ m\widehat{GJ}=29 \end{gathered}[/tex]
The measure of arc GJ is 29 degrees.
