Question

Choose an equation for the relationship between the measures of the angles and arcs.

Answer 1

Because ∠2 is a diameter away from arc ST, ST is two times larger than ∠2. So, the answer is:

m∠2 = 1/2(mST)

Answer 2

Inscribed angles (angles on the line of the circle) are one half of its opposite arcs.
Therefore m <2 = 1/2 (mST), the 2nd one down (or middle) answer.
For example, if ST were 80°, then m <2 would be 40°.