Answer :

Answer:

  a.  27.5°

Step-by-step explanation:

You want the measure of external angle U formed by tangent UR and secant US, given ∠S = 24° and arc RS = 103°.

Inscribed angle

The inscribed angle RST is half the measure of the intercepted arc RT, so ...

  arc RT = 2·∠S = 2·24° = 48°

External angle

External angle U is half the difference of the intercepted arcs.

  ∠U = (arc RS -arc RT)/2 = (103° -48°)/2 = 55°/2

  ∠U = 27.5° . . . . choice A