# In the trapezoid ABCD AB = CD, ∠BDA = 67 ° and ∠BDC = 28 °. Find the angle ABD

May 31, 2020 | Education

| ∠ADC = ∠BDA + ∠BDC = 67 ° + 28 ° = 95 °

Because AB = CD, then the trapezoid ABCD is isosceles.

Then ∠ADC = ∠BAD = 95 ° (by the property of an isosceles trapezoid).

Consider the triangle ABD:

By the theorem on the sum of the angles of a triangle:

180 ° = ∠BAD + ∠ADB + ∠ABD

180 ° = 95 ° + 67 ° + ∠ABD

∠ABD = 18 °

Answer: 18

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