Question

find the value of ( x ).

Explanation:

Step1: Recall external 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:
$$x = \frac{1}{2} \times (\text{measure of larger arc} - \text{measure of smaller arc})$$

Step2: Substitute given arc values

The larger intercepted arc is $\overset{\frown}{EA} = 98^\circ$, and the smaller intercepted arc is $\overset{\frown}{DB} = 40.2^\circ$. Substitute these into the formula:
$$x = \frac{1}{2} \times (98 - 40.2)$$

Step3: Calculate the difference first

Compute the value inside the parentheses:
$$98 - 40.2 = 57.8$$

Step4: Compute half the difference

Divide the result by 2:
$$x = \frac{57.8}{2} = 28.9$$

Answer:

$28.9$