The big bang theory is an expansion of the space, not an explosion. It happened around 13.7 billion years ago.
Pangea is a supercontinent that existed during the late Paleozoic era but it started to break apart around 175 million years ago. A theory called plate tectonics was accepted in the early 1960s that explained the rock movement on the Earth's surface. Around 250 million years ago plate tectonic pull all of the continents together to form Pangea and the reasons why it breaks apart. Scientists look at the boundary region of the plate (plate boundaries) that form our continents and upon their knowledge/observation they come up with three kinds of plate boundaries, divergent, convergent, and transform. Divergent is where plates move away. Convergent is where plates go towards each other. Transform is where plates slide along each other. Pangea is probably formed by the convergent boundaries. It probably breaks apart because of the divergent. boundaries.
Geologic Time Scale is somewhat of a calendar of the Erath's history that based on the evidence of the rock's layer/formation and the fossil that lie in the rocks. It's organized into 4 subdivisions, Precambrian, Paleozoic, Mesozoic, and Cenozoic. The Geologic Time Scale is not based on years but instead the organism that lived in that period.