Answer:
[tex]x=6[/tex]
Step-by-step explanation:
The lengths of line segments [tex]\overline{AB}[/tex] and [tex]\overline{AC}[/tex] because of the two segments and two angles marked as equal in the diagram. Because of this, the arcs [tex]\widehat{AB}[/tex] and [tex]\widehat{AC}[/tex] are equal.
Since there are 360 degrees in a circle, we can now set up the following equation:
[tex](10x-23)+(10x-23)+106=180,\\20x-46+106=180,\\20x+60=180,\\20x=120,\\x=\boxed{6}[/tex]
