With the help of a protractor we will find the measure of ∠Q.
As we can see, m∠Q = 50^(∘). Now, by the Arc Addition Postulate, we can write the following equation and solve if for one of the measures.
mACB + mAB = 360^(∘)
⇓
mAB = 360^(∘) - mACB
Now, since the two tangent lines intersect each other outside the circle, the measure of ∠Q is half the measure of the difference of the intercepted arcs.
m∠Q = 1/2(mACB - mAB)
Let's substitute the expression we found for mAB and m∠Q into the equation above.
With this measure, let's find the measure of the minor arc.
mAB = 360^(∘) - mACB^(230^(∘))
⇓
mAB = 130^(∘)
To summarize, let's mark all the measures in our diagram.
