Suppose we are given two straight lines \(AB\) and \(CD\), and suppose they both cut each other at point \(E\):
An angle on a straight line is 180˚, so \(\angle AEC + \angle AED = 180˚\).
An angle on a straight line is 180˚, so \(\angle AED + \angle BED = 180˚\).
This means \(\angle AEC + \angle AED = \angle AED + \angle BED\). Subtracting \(\angle AED\) from both sides gives us \(\angle AEC = \angle BED\).