Final answer:
Following World War I, Palestine, Iraq, and Transjordan came under British control, as they were included in the British mandates established by international agreements.
Step-by-step explanation:
Palestine, Iraq, and Transjordan came under the control of the United Kingdom following the dissolution of the Ottoman Empire at the end of World War I. The Sykes-Picot Agreement, a covert deal made between Britain and France, divided the Middle Eastern areas under two spheres of influence. The British mandate covered the areas of Iraq, Palestine, and Transjordan, with the French mandate covering Syria and Lebanon. The British, with their control of these territories, had conflicting promises to fulfil. They supported the establishment of a Jewish homeland in Palestine as stated in the Balfour Declaration of 1917, while also having assured Arab leaders of their support for an independent Arab nation.