Answer:
The correct option is c.
Step-by-step explanation:
Given information: The measure of arc AXC is 235°. Let the center of the circle be O.
The sum of all disjoint arcs is 360°. So,
[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]
[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]
[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]
[tex]Arc(AC)=125^{\circ}[/tex]
[tex]\angle AOC=125^{\circ}[/tex]
The measure of arc AC is 125°.
Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.
[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]
[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]
[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]
[tex]\angle ABC=55^{\circ}[/tex]
The measure of angle ABC is 55°. Therefore the correct option is c.
