MX₆ is a molecule with octahedral geometry. How many X – M – X bonds are at 180°?

The correct option is three.

To understand why, let us examine the geometry of an octahedral molecule, denoted as MX₆, where M is the central atom and X represents the six surrounding atoms (ligands). In a regular octahedral arrangement, the central atom M is positioned at the center, and the six X atoms are located at the six vertices of a regular octahedron.

This layout can be visualized by placing the central M atom at the origin of a three-dimensional Cartesian coordinate system (x, y, and z axes):
- Four X atoms lie in a horizontal plane (the square plane), with one pair along the x-axis and another pair along the y-axis.
- The remaining two X atoms lie along the vertical z-axis, with one atom directly above and one directly below the square plane.

A bond angle of
$180°$
represents a perfectly straight line passing through the central M atom, connecting two diagonally opposite X atoms (X - M - X). Let us count these collinear pairs along the coordinate axes:
1. Along the x-axis: The two opposite equatorial X atoms form one linear X - M - X bond.
2. Along the y-axis: The other two opposite equatorial X atoms form a second linear X - M - X bond.
3. Along the z-axis: The two axial X atoms (top and bottom) form a third linear X - M - X bond.

Since the three coordinate axes are mutually perpendicular, there are exactly three pairs of opposite X atoms. Therefore, there are exactly three X - M - X bonds at
$180°$
in an octahedral molecule.