Question

find the value of ( x ), where ( x^circ = moverarc{bd} ).

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. The formula is:
$$m\angle C = \frac{1}{2}(m\overset{\frown}{AE} - m\overset{\frown}{BD})$$

Step2: Substitute known values

We know $m\angle C = 37^\circ$, $m\overset{\frown}{AE} = 130^\circ$, and $m\overset{\frown}{BD} = x^\circ$. Substitute into the formula:
$$37 = \frac{1}{2}(130 - x)$$

Step3: Solve for x

Multiply both sides by 2:
$$74 = 130 - x$$
Rearrange to isolate x:
$$x = 130 - 74$$
$$x = 56$$

Answer:

$56$