Question

find the value of ( x ). note that, in the image below, ( moverarc{aed} = 208^circ ) and ( moverarc{bd} = 96^circ ).

Explanation:

Step1: Find arc $\overparen{AB}$

First, calculate the measure of the remaining arc of the circle. The total degree of a circle is $360^\circ$.
$$m\overparen{AB} = 360^\circ - m\overparen{AED} - m\overparen{BD} = 360^\circ - 208^\circ - 96^\circ = 56^\circ$$

Step2: Calculate angle $x$

Use the outside 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.
$$x = \frac{1}{2}(m\overparen{AED} - m\overparen{BD}) = \frac{1}{2}(208^\circ - 96^\circ)$$
$$x = \frac{1}{2}(112^\circ) = 56^\circ$$

Answer:

$56$