Molecular geometry of methane ($\text{CH}_4$):

• Linear geometry ($180^\circ$) occurs in $sp$-hybridized molecules such as $\text{CO}_2$ or acetylene.
• In methane ($\text{CH}_4$), the central carbon atom undergoes $sp^3$ hybridization with four equivalent bonding electron pairs directed toward the corners of a regular tetrahedron, yielding a tetrahedral geometry with bond angles of $109.5^\circ$.
• Trigonal planar geometry ($120^\circ$) occurs in $sp^2$-hybridized molecules like boron trifluoride ($\text{BF}_3$).
• Trigonal pyramidal geometry ($107^\circ$) occurs when an $sp^3$-hybridized central atom possesses one lone pair, such as in ammonia ($\text{NH}_3$).

Endosymbiotic theory of organellar evolution:

• Mitochondria originated from engulfed aerobic alpha-proteobacteria, possessing circular dsDNA, 70S ribosomes, and binary fission similar to prokaryotes.
• Chloroplasts originated from engulfed photosynthetic cyanobacteria, likewise possessing circular dsDNA, 70S ribosomes, and prokaryotic-type division proteins (FtsZ).
• The nucleus is an exclusively eukaryotic defining organelle with linear chromosomes and 80S cytosolic translation machinery.
• The Golgi apparatus is an exclusively eukaryotic endomembrane organelle.

Cytoskeletal filament composition:

• Tubulin is a globular protein that polymerizes into heterodimers ($\alpha$- and $\beta$-tubulin) to form microtubules ($25\text{ nm}$ in diameter).
• Microfilaments (approx. $7\text{ nm}$ in diameter) are solid helical cytoskeletal fibers assembled by the polymerization of globular G-actin monomers into filamentous F-actin polymers.
• Myosin is an ATP-dependent motor protein that interacts with actin filaments to generate contractile force.
• Ribosomes are protein-RNA complexes for protein translation, not cytoskeletal proteins.