High On Potenuse

The angle is 60° because it is an equilateral triangle which is same as sin^-1(sqrt3/2)

Each side of the triangle is a diagonal of identical sized squares, so they are all the same length, so it must be an equalatrial triangle, so each angle is 60 degrees.

But, despite asking for the answer in degrees, the answers are not in degrees. If you don't happen to know what sin 60 is, you might have to use a calculator at this point...

I thought that a solution based on vectors should be there , so here I am !

Assume the length of each edge be a units .

The position vectors of the points A,B and C are given in the pic . Let the origin be O .

$\vec{AB} = \vec{B} - \vec{A} = (-a,a,0)$

$\vec{AC} = \vec{C} - \vec{A} = (0,a,-1)$

Now lets take the dot product of $\vec{AB}$ and $\vec{AC}$ since we are interested in knowing the angle between them .Let the angle be $\theta$

$\vec{AB} \cdot \vec{AC} = |\vec{AB}| |\vec{AC}| \cos \theta \\ \Rightarrow \cos \theta = \dfrac{0 + a^{2} + 0}{\sqrt{a^{2}+a^{2}+0} \sqrt{0+a^{2} + a^{2}}} \\= \frac{1}{2}$

Hence the answer is $\arccos \frac{1}{2} = \arcsin \frac{\sqrt{3}}{2}$

If you complete the triangle by adding the 3rd red line, each of the sides is a hypotenuse of a face of the cube. So it's an equilateral triangle, meaning each angle is $60^{o}$ . Since $\sin 60=\frac{\sqrt{3}}{2}$ , the answer is C.

No need to explain an equilateral triangle in such detail. The diagonals of a cube are all the same length so the triangle edges are all the same length. Therefore it has to be an equilateral triangle

None of the above, since none allow for the specified answer in degrees

The two red lines are two sides of an equilateral triangle

So the measure of the required angle is 60

Draw one more diagonal on the top face connecting the existing red ones. Now it will create an equilateral triangle so angle is 60° i.e. first option.

Each side length of the triangle is sqrt(2) so it is equilateral and each angle is 60 degrees. Simplicity is key.

equilateral triangle, therefore 60 deg

If you join the 3 diagonals of any 3 mutually adjacent faces of a cube, the diagonals form an equilateral triangle.

If I join the end points of those two lines, it will become an equilateral triangle as even after joining endpoints length will remain same as those of other two lines !!

Simply the angle is 60 degree

As the question just state it's a cube, so the sides must be equal ( based on the property of diagonals in a square).

If the cube side length is "a", then length of each red line is \sqrt{a} . similarly the distance bet two ends of the red lines is also \sqrt{a} . Thus it forms an equilateral triangle. And thus angle bet two red lines is 60degree.