Answer
Angle = 70.5 $^{\circ}$ or 109.5 $^{\circ}$. These two answers are supplementary (add up to 180 $^{\circ}$), so the answer depends on which one you decided to find.
Work Step by Step
Start with a cube with side lengths 1, and vertices ABCDEFGH as shown on the diagram. Construct vectors a,c, and d as defined in the diagram. Construct them in x,y,z components; and find their lengths which all equate to $\sqrt 3$.
Two situations are discussed: the angle between vectors a and c, and the angle between vectors a and d. Using the dot product in component and abstract form, you work out the angles.
