Answer:
f = 50 degrees
g = 40 degrees
Step-by-step explanation:
Triangle ABC is isosceles as AB = AC as they are both tangents that exit from the same external point to the same circle.
Therefore, <A = <C = f.
The sum of all angles in a triangle is 180 degrees, therefore:
[tex]80 + f + f = 180\\2f = 100\\f = 50 \text{ degrees}[/tex]
<OAB is a right angle as a tangent line to a circle is perpendicular to the radius of that circle in the point of intersection.
<OAB is made of <OAC = g and <CAB (= f = 50 degrees), therefore <OAC (= g) is simply the difference between <OAB and <CAB:
[tex]< \text{OAC} = < \text{OAB}- < \text{CAB}\\\to g = 90 - f\\\to g = 90 - 50 = 40 \text{ degrees}[/tex]
