The Inscribed Angle Theorem gives us some information about m∠ T and m∠ S.
m∠ T = 12mURS & (I) m∠ S = 12mTUR & (II)
Recall that we are given that m∠ T = 12m∠ S. Let's substitute it into the left-hand side of Equation (I).
1/2m∠ S = 1/2mURS
⇓
m∠ S = mURS
Next, we substitute the last equation into Equation (II) and get the desired result.
Given: & m∠ T = 12m∠ S
Prove: & mTUR = 2mURS
Proof: By the Inscribed Angle Theorem, m∠ T = 12mURS and m∠ S = 12mTUR. Substituting the given equation in the first one gives m∠ S = mURS. Finally, we substitute this equation into the second one and multiply both sides by 2 to get mTUR = 2mURS.
