213,305 views
40 votes
40 votes
Please help
maths geometry

Please help maths geometry-example-1
User Dogs
by
2.3k points

1 Answer

17 votes
17 votes

Answer:

D₁ = 68°

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°

User Sandun Madola
by
3.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.