Question

what is the measure of $\angle dfh?$
a. $47^\circ$
b. $53^\circ$
c. $43^\circ$
d. $86^\circ$

Explanation:

Step1: Recall secant angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs are $\overset{\frown}{DH}=133^\circ$ and $\overset{\frown}{EG}=47^\circ$.

Step3: Calculate the angle

Substitute into the formula: $\angle DFH = \frac{1}{2} \times (\overset{\frown}{DH} - \overset{\frown}{EG})$
$\angle DFH = \frac{1}{2} \times (133^\circ - 47^\circ) = \frac{1}{2} \times 86^\circ = 43^\circ$

Answer:

C. $43^\circ$