Question

find the value or measure. Assume all lines that appear to be tangent are tangent. m(angle) FHG=

Answer 1

Assuming that the lines FG and HG are tangent, you need to remember that, by definition, when two tangents intersect outside a circle, the angle formed by them is the difference of the intercepted arcs divided by 2.

Then:

$AngleFormedbyTwoTangents=\frac{(DifferenceOfInterceptedArcs)}{2}$

In this case, you know that the angle formed by the tangents FG and HG is:

$\angle FGH$

And the Intercepted arcs are the following:

$\begin{gathered} FH=97\degree \\ FIH \end{gathered}$

By definition, a circle has 360 degrees; then you can find the measure of the arc FIH as following:

$\begin{gathered} FIH=360\degree-97\degree=263\degree \\ \end{gathered}$

Knowing that, you can substitute values into the equation in order to find the measure of the angle FGH:

$m\angle FGH=\frac{263\degree-97\degree}{2}=83\degree$

The answer is: First option.