Answer: [tex]x=115\°[/tex]
Step-by-step explanation:
Observe in the figure that the angle "x" is formed by two intersecting chords in the circle.
By definition:
[tex]Angle\ formed\ by\ two\ intersecting\ Chords=\frac{1}{2}(Sum\ of\ Intercepted\ Arcs)[/tex]
In this case you know that the Intercepted Arcs are:
[tex]AD=140\°\\BC=90\°[/tex]
Then, you know that:
[tex]x=\frac{1}{2}(AD+BC)[/tex]
Finally, substituting values into the formula and evaluating, you get that the measure of the angle "x" is:
[tex]x=\frac{1}{2}(140\°+90\°)\\\\x=\frac{1}{2}(230\°)\\\\x=115\°[/tex]
