Ajay is standing at point $A$ near Pontianak, Indonesia, $0^{\circ}$ latitude and $110^{\circ} \text{ E}$ longitude. Billy is standing at point $B$ near Big Baldy Mountain, Idaho, USA, $45^{\circ} \text{ N}$ latitude and $115^{\circ} \text{ W}$ longitude. Assume that the Earth is a perfect sphere with center $C.$ What is the degree measure of $\angle ACB$ ?

105
$112 \dfrac{1}{2}$
150
120
135

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