Respuesta :

mhanifa

Answer:

  • 10°

Step-by-step explanation:

Given trapezoid ABCD, where:

  • AB ║ DC
  • AB = AD
  • m∠BAD = 160°
  • m∠BDC = ?

Since AB and DC are parallel, the diagonal BD is transversal and:

  • ∠ABD ≅ ∠BDC

Consider ΔABD

Since its two sides are equal, it is isosceles hence ABD and ADB are equal angles:

  • m∠ABD = 1/2(180 - 160) = 1/2(20) = 10°
  • m∠BDC = m∠ABD = 10°

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