See Soroban's post #5

1) I assume that this is to be set up like a geometric proof, so here goes:

1.

A central angle is equal to the measure of its intercepted arc.

2.

An inscribed angle is equal to one-half the measure of its intercepted arc.

3.

Given

4.

Substitution using steps 2 and 3.

5.

Addition using steps 2 and 4.

6.

Addition of step 5

7.

Substitution using steps 1 and 6

8.

Symmetric property of equality