Answer:
[tex]m\angle b=97^{\circ},\\m\angle c= 97^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are angles on opposites sides of an intersection of two lines. Therefore, [tex]\angle c[/tex] and [tex]\angle b[/tex] are vertical angles. Similarly, the angle opposite to the angle marked 83 degrees is also equal to 83 degrees. Vertical angles are always equal.
Since there are 360 degrees in a circle, we have the following equation:
[tex]\angle c+\angle b+83+83=360,\\2\angle c+166=360,\\2\angle c=194,\\\angle c=\frac{194}{2}=\boxed{97^{\circ}}[/tex]
Since [tex]\angle c[/tex] and [tex]\angle b[/tex] are vertical angles and vertical angles are also equal, the measure of angle [tex]b[/tex] is also [tex]\boxed{97^{\circ}}[/tex]
