The measure of an angle formed by a secant and a tangent drawn from an external poi...
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Problem
The measure of an angle formed by a secant and a tangent drawn from an external point to a circle.
Step-by-step solution
The angle $\angle DFH$ is formed by secant FD and secant FH. The measure of $\angle DFH$ is half the difference of the intercepted arcs. The intercepted arcs are arc DH and arc EG. The measure of arc DH is $133^{\circ}$. The measure of arc EG is $47^{\circ}$. Therefore, $\angle DFH = \frac{1}{2}(133^{\circ} - 47^{\circ}) = \frac{1}{2}(86^{\circ}) = 43^{\circ}$.
Answer
$43^{\circ}$