Answer: [tex]x=115\°[/tex]
Step-by-step explanation:
As you can observe in the figure, the angle "x" is formed by two intersecting chords in the circle.
It is important to remember that, by definition:
[tex]Angle\ formed\ by\ two\ intersecting\ Chords=\frac{1}{2}(Sum\ of\ Intercepted\ Arcs)[/tex]
In this case you can identify that the Intercepted Arcs are:
[tex]AD=140\°\\BC=90\°[/tex]
Then:
[tex]x=\frac{1}{2}(AD+BC)[/tex])
Therefore, 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]
