This thesis describes measurements of rare electroweak penguin decays performed with data collected by the Large Hadron Collider beauty experiment corresponding to 3 fb^{-1} of integrated luminosity. The purpose of these measurements is to search for physics beyond the theoretical framework known as the Standard Model (SM). Electroweak penguin decays are sensitive to virtual particles in extensions to the SM whose influence on the decay amplitude can be of similar strength to the SM contribution. The particular measurements that are described in this thesis are the differential branching fractions and isospin asymmetries of B -> K(*) μ^+ μ^- decays as well as the angular observables in B -> K μ^+ μ^- decays. Although results are consistent with the SM, all the branching fractions of B -> K(*) μ^+ μ^- decays tend to favour a lower value than theoretical predictions.