What are the shapes of ethyne and methane?

Ethyne $\left(\mathrm{C}_2 \mathrm{H}_2\right)$ Number of $\sigma$-bonds at $\mathrm{C}$-atom $=2$ Number of lone pair of electrons at $\mathrm{C}$-atom $=0$ $\therefore$ Total $=2+0=2$ $\therefore$ Hybridisation is $\mathrm{sp}$. $\therefore \mathrm{C}_2 \mathrm{H}_2$ is linear Methane $\left(\mathrm{CH}_4\right)$ Number of $\sigma$ bonds at $\mathrm{C}$-atom $=4$ Number of-lone pair of electrons at C-atom $=0$ $\therefore$ Total $=4+0=4$ $\therefore$ Hybridisation is $\mathrm{sp}^3$. $\therefore \mathrm{CH}_4$ is tetrahedral.