Question

find m∠efg
72
147
41
38

Explanation:

Step1: Recall exterior secant angle formula

The measure of an angle formed by two secants intersecting outside a circle is half the difference of the measures of the intercepted arcs. The formula is:
$$m\angle EFG = \frac{1}{2}(m\overset{\frown}{DH} - m\overset{\frown}{EG})$$

Step2: Substitute given arc measures

We know $m\overset{\frown}{DH}=121^\circ$ and $m\overset{\frown}{EG}=39^\circ$.
$$m\angle EFG = \frac{1}{2}(121^\circ - 39^\circ)$$

Step3: Calculate the difference first

$$121^\circ - 39^\circ = 82^\circ$$

Step4: Find half the difference

$$m\angle EFG = \frac{1}{2}(82^\circ) = 41^\circ$$

Answer:

41