Final answer:
Angelique is requesting active voluntary euthanasia from her doctor, a process which involves administering medication to end her life painlessly due to terminal cancer.
Step-by-step explanation:
Angelique is requesting her doctor to perform euthanasia. Euthanasia is a process where an individual's life is ended in order to relieve them of suffering, especially in the case of terminal illnesses. Angelique's condition has progressed to the final stages, and the cancer has metastasized to her lungs and other organs, indicating a poor prognosis. The type of euthanasia she is seeking is likely active voluntary euthanasia, where a consented medication is administered by a healthcare professional, leading to a painless death. This act is intended to offer dignity and relief from intense pain in her last moments.