Consider the parallelogram below. We mark the bottom-left angle with a and the bottom-right angle with b to denote their measures as shown in Figure 1.
We create another parallelogram with same size and the shame shape, but of different color. We place the two parallelograms side by side as shown in Figure 2. The angles a and b is a linear pair; therefore, (1) a + b = 180˚
We create two more parallelograms and place them as shown in Figure 3 to form a bigger parallelogram. Angle a in the red parallelogram and the adjacent angle in the blue parallelogram is also a linear pair; therefore, the upper-left angle in the blue parallelogram also equals b (see Figure 4). In effect, the the upper-right angle in the yellow parallelogram also equals the measure of angle a. » Read more