In the diagram provided, the angle at the vertex (angle G) is half the measure of its intercepted arc, (arc HF). Therefore we have;
[tex]\begin{gathered} 10x=\frac{1}{2}(21x-3) \\ 10x=\frac{(21x-3)}{2} \\ \text{Cross multiply and you have;} \\ 2(10x)=21x-3 \\ 20x=21x-3 \\ \text{Collect all like terms,} \\ 20x-21x=-3 \\ -x=-3 \\ \text{Multiply both sides by -1,} \\ x=3 \end{gathered}[/tex]
Therefore, when x = 3, arc HF is now derived as follows;
[tex]\begin{gathered} HF=21x-3 \\ HF=21(3)-3 \\ HF=63-3 \\ HF=60 \end{gathered}[/tex]
Arc HF measures 60 degrees
