In a convex quadrilateral ABCD AB = BC, AD = CD, angle B = 3 degrees, angle D = 39 degrees. Find angle A.

Let’s connect points A and C with a segment AC.
Since AB = BC, then Δ ABC is isosceles, therefore ∠ BAC = ∠ BCA.
Similarly, Δ АDС is isosceles and ∠ DАC = ∠ DСА.
In any triangle, the sum of the interior angles is 180 °.
Using this fact, we get: ∠ BAC + ∠B + ∠ BCA = 180 ° or 2 * ∠ BAC = 180 ° – 3 °, whence ∠ BAC = 88.5 °.
Similarly, ∠ DAC = 70.5 °.
So, ∠ BAD = ∠ BAC + ∠ DAC = 88.5 ° + 70.5 ° = 159 °.
Answer: 159 °.