A3. In triangle $A B C$, the bisectors of angle $\angle B A C$ and angle $\angle C B A$ intersect at point $T$. Let $\gamma$ be the measure of angle $\angle A C B$. What is the measure of angle $\angle A T B$?
(A) $2 \gamma$
(B) $180^{\circ}-\gamma$
(C) $360^{\circ}-4 \gamma$
(D) $60^{\circ}+\gamma$
(E) $90^{\circ}+\frac{\gamma}{2}$

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A3. Choose $\Varangle A T B=180^{\circ}-\Varangle B A T-\Varangle T B A=180^{\circ}-\frac{\alpha}{2}-\frac{\beta}{2}=180^{\circ}-\frac{1}{2}(\alpha+\beta)$. Since $\alpha+\beta+\gamma=180^{\circ}$, it follows that $\alpha+\beta=180^{\circ}-\gamma$. Therefore, $\Varangle A T B=180^{\circ}-\frac{1}{2}\left(180^{\circ}-\gamma\right)=90^{\circ}+\frac{\gamma}{2}$. The correct answer is $E$.