The definition of parallelogram is that both pairs of opposing sides are parallel. However, they have other properties:
0. Both pairs of opposite sides are congruent.
,1. Both pairs of opposite angles are congruent.
,2. Diagonals bisect each other.
,3. One pair of opposite sides are congruent AND parallel.
Based on the properties of parallelograms, we know that ∠A is congruent to ∠C. Therefore if we divide the figure into two triangles as follows, m∠A will be divided into two.
As m∠A is the same as m∠C, then when dividing them by two, the final answer will be the same. For example, if m∠A = 60°, m∠C = 60° , then:
[tex]\frac{m\angle C}{2}+\frac{m\angle A}{2}=\frac{60}{2}+\frac{60}{2}=30+30=60[/tex]Then, as the measure of the interior angles of a triangle is equal to 180°, then:
[tex]m\angle D=180-\frac{m\angle C}{2}-\frac{m\angle A}{2}[/tex]Based on the latter, we can conclude that one angle is supplementary to both consecutive angles.
