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

Find the value or measure. Assume all lines that appear to be tangent are tangent-example-1
User Kalher
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1 Answer

16 votes
16 votes

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=((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=(263\degree-97\degree)/(2)=83\degree

The answer is: First option.

User Noich
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