We want to find mGJF. We know that if a secant and a tangent intersect at the point of tangency, then the measure of the each angle formed is one half the measure of the intercepted arc.
m∠G = 1/2(mFG)
Note that arcs FG and GJF form together a full turn around the origin. By the Arc Addition Postulate, we can write an expression for mFG and use it to find mGJF.
mFG = 360^(∘) - mGJF
↓
m∠G = 1/2(360^(∘) - mGJF)
Let's substitute the known value for m∠G and solve it for mGJF .
