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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