We have been given two secants and their intercepted arc measures and we are asked to find the measure of angle x.
In order to find measure of angle x we will use circle's two intersecting secants from a point theorem. This theorem tells us that measure of an angle formed by two secants drawn from an outside point equals to half the difference of intercepted arcs.
[tex]m\angle x=\frac{1}{2}(\widehat{\text fararc }-\widehat{\text near arc})[/tex]
Now substituting given values in our formula we will get
[tex]m\angle x=\frac{136^{0}-28^{0}}{2}=\frac{108^{0}}{2}=54^{0}[/tex]
Therefore, measure of angle x is 54 degrees.
