Respuesta :

Solution:

Let the missing angle be x.

It should be noted:

  • The two diagonals form four isosceles triangles. (ΔBOC, ΔCOD, ΔDOA, and ΔAOB)
  • ∠DOA = ∠BOC = 44 (Vertically opposite angles)
  • Interior angles of a triangle sum up to 180°

This means that...

  • 44 + x + x = 180

Combine like terms.

  • 44 + 2x = 180

Subtract 44 both sides.

  • 2x = 180 - 44

Simplify the RHS

  • 2x = 136

Divide 2 both sides.

  • 2x/2 = 136/2
  • => x = 136/2 = 68°

Answer:

68°

Step-by-step explanation:

Remember :

  • The diagonals of a rectangle are equal
  • Hence, they will have equal angles on the corners of the shape

Solving :

  • ∠DOA = ∠COB = 44° (Vertically Opposite Angles)
  • Now, consider ΔDOA
  • ∠ODA = ∠OAD (Because angles opposing equal side lengths are equal)
  • ∠ODA + ∠OAD + ∠DOA = 180° (Angle Sum Property)
  • 2∠OAD + ∠DOA = 180°
  • 2∠OAD + 44° = 180°
  • 2∠OAD = 136°
  • ∠OAD = 68° (missing angle value)

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