# In trapezoid ABCD, AB = CD, Angle BDA = 54, Angle BDC = 33. Find the angle ABD.

August 30, 2021 | education

| Determine the value of the angle ADC.

Angle ADC = BDA + BDC = 54 + 33 = 87.

Since, by condition, AB = CD, the trapezoid ABCD is isosceles, then the angle BAD = ACD = 87.

In triangle ABD we define the value of angle ABD. The sum of the inner angles of the triangle is 180, then the angle ABC = (180 – BAD – BDA) = (180 – 87 – 54) = 39.

Answer: The angle ABD is 39.

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