A skeletal formula draws cyclohexane as a flat hexagon. The real molecule folds into what chemists call a chair.
Each corner of a flat hexagon is 120°. Each carbon in cyclohexane has 4 single bonds, 2 to carbons and 2 to hydrogens, so its bonds, just like methane's, spread out toward the corners of a tetrahedron, about 109.5° apart. A flat ring would force every C–C–C angle open to 120°. So the ring puckers: the carbon at one end of the chair tips up, the carbon at the other end tips down, and every angle settles at about 111°, close to methane's.
The fold gives the hydrogens room too. On each carbon, one hydrogen points straight up or straight down, taking turns round the ring, and the other points outward around the ring's edge. Hydrogens on neighbouring carbons sit staggered, out of each other's way.
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