Answer
$CH_{4}$ and $H_{2}O$ both have same bond angles due to the same number of electron pairs.
Work Step by Step
In both of the molecules, central atoms have four electron pairs. In $CH_{4}$ all the electron pairs are bonded, however, in $H_{2}O$ two electron pairs are bonded and two pairs are non-bonded. Both molecules have tetrahedral shape of electron groups with bond angles of 109 degree.
