Question

Please help maths geometry

Answer 1

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°.

Opposite sides of a parallelogram are parallel.

Using the Alternate Interior Angles Theorem:

A₂ = E₁ = 28°

Therefore, A = A₁ + A₂ = 28° + 28° = 56°

Opposite angles in a parallelogram are equal.

Therefore, C = A = 56°.

Opposite sides of a parallelogram are equal in length, 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°