# In the trapezoid ABCD AB = CD, ∠BDA = 35 ° and ∠BDC = 58 °. Find the angle ABD.

May 31, 2020 | Education

| ∠ADC = ∠BDA + ∠BDC = 35 ° + 58 ° = 93 °.

The trapezoid ABCD is isosceles (because AB = CD), therefore, by the property of an isosceles trapezoid, ∠BAD = ∠ADC = 93 °.

Consider the triangle ABD:

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

180 ° = ∠BAD + ∠ABD + ∠BDA

180 ° = 93 ° + ∠ABD + 35 °

∠ABD = 180 ° -93 ° -35 °

∠ABD = 52 °

Answer: 52

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