Before we can solve the length of the missing sides and measure of the missing angles, it is important to note some properties of a parallelogram.
1. The opposite angles are congruent. (∠A≅∠C, ∠B≅∠D)
2. The consecutive angles are supplementary. (∠A + ∠D = 180, ∠A + ∠B = 180, etc.)
3. The opposite sides of a parallelogram are parallel and congruent. (AD = BC, AB = DC)
4. Diagonals bisect each other. (AE = EC, DE = EB)
Based on the 2nd property, we know that ∠A + ∠D = 180°. In the question, ∠A = 120° hence, ∠D = 180° - 120° = 60°.
In the diagram, we can see that ∠D = ∠ADB + ∠BDC and the measure of ∠ADB is 43°. Let's solve for the measure of ∠BDC.
[tex]\begin{gathered} \angle D=\angle ADB+\angle BDC \\ 60=43+\angle BDC \\ 60-43=\angle BDC \\ 17=\angle BDC \end{gathered}[/tex]
Hence, the measure of ∠BDC is 17°. Since ∠BDC and ∠ABD are alternating interior angles, the measure of ∠ABD is also 17°.
Lastly, based on the 4th property which states that diagonal bisect each other, the measure of AE is equal to the measure of EC. Since EC is 7 units, AE is also 7 units.
