Measurement of angular asymmetries in the decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mo>ℓ</mml:mo><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mo>ℓ</mml:mo><mml:mo>−</mml:mo></mml:msup></mml:math>

We study the lepton forward-backward asymmetry ${\mathcal{A}}_{FB}$ and the longitudinal ${K}^{*}$ polarization ${F}_{L}$, as well as an observable ${P}_{2}$ derived from them, in the rare decays $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, where ${\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ is either ${e}^{+}{e}^{\ensuremath{-}}$ or ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, using the full sample of 471 million $B\overline{B}$ events collected at the $\mathrm{\ensuremath{\Upsilon}}(4S)$ resonance with the BABAR, detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ collider. We separately fit and report results for the ${K}^{*0}(892){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ and ${K}^{*+}(892){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ final states, as well as their combination ${K}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, in five disjoint dilepton mass-squared bins. An angular analysis of ${B}^{+}\ensuremath{\rightarrow}{K}^{*+}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays is presented here for the first time.