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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