Answer:
D₁ = 68°
Step-by-step explanation:
If AB = BE then ΔABE is an isosceles triangle, therefore A₁ = E₁.
If A₁ = 28° then E₁ = 28°.
<u>Opposite sides</u> of a parallelogram are <u>parallel</u>.
Using the Alternate Interior Angles Theorem:
A₂ = E₁ = 28°
Therefore, A = A₁ + A₂ = 28° + 28° = 56°
<u>Opposite angles</u> in a parallelogram are <u>equal</u>.
Therefore, C = A = 56°.
<u>Opposite sides</u> of a parallelogram are <u>equal in length</u>, so AB = CD.
If AB = DE = CD then ΔCDE is an isosceles triangle.
Therefore, C = E₃ = 56°.
Interior angles of a triangle sum to 180°.
⇒ D₁ + C + E₃ = 180°
⇒ D₁ + 56° + 56° = 180°
⇒ D₁ + 112° = 180°
⇒ D₁ = 180° - 112°
⇒ D₁ = 68°
