Question

pls help! Find the measure of the arc or angle indicatedFind the measure of arc HFa) 45°b) 60°c) 75°d) 53°

Answer 1

In the diagram provided, the angle at the vertex (angle G) is half the measure of its intercepted arc, (arc HF). Therefore we have;

`\begin{gathered} 10x=(1)/(2)(21x-3) \\ 10x=((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}`

Therefore, when x = 3, arc HF is now derived as follows;

`\begin{gathered} HF=21x-3 \\ HF=21(3)-3 \\ HF=63-3 \\ HF=60 \end{gathered}`

Arc HF measures 60 degrees