Final answer:
The artery responsible for supplying the bladder, rectum, and some reproductive organs is the internal iliac artery, which branches off from the common iliac arteries.
Step-by-step explanation:
The major artery that supplies the bladder, rectum, and some reproductive organs is called the internal iliac artery.
Branching from the common iliac arteries, which are a continuation of the abdominal aorta, the internal iliac artery plays a crucial role in providing blood to the urinary bladder, walls of the pelvis, external genitalia, and the medial portion of the femoral region. Specifically, in females, the internal iliac artery also supplies blood to the uterus and vagina.