\(NH _2^{-}\) has \(2\) bond pairs and \(2\) lone pairs of electrons.
\(NH _3\) has \(3\) bond pairs and \(1\) lone pair.
\(NH _4^{-}\) has \(4\) bond pairs.
Bond pair - Bond pair electron repulsions \(\,<\,\) Bond pair - Lone pair electron
repulsions \(\,<\,\) Lone pair - Lone pair electron repulsions
Greater lone pair - lone pair repulsions among electrons causes the \(H - N - H\)
bond angle to decrease. This effect is greatest for \(NH _2^{-}\), followed by \(NH _3\).
Hence, the correct order is: \(NH _4^{+}\,>\, NH _3\,>\, NH _2^{-}\)