The circle can be described only near an isosceles trapezoid (by the trapezoid property).
It turns out that our trapezoid is isosceles (or isosceles).
Let 49 ° be the angle BAD.
∠BAD = ∠ADC = 49 ° (by the property of an isosceles trapezoid).
The sum of the angles of a convex n-gon is calculated by the formula (n-2) 180 °, then the sum of the angles of the trapezoid is (4-2) 180 ° = 360 °.
360 ° = ∠BAD + ∠ADC + ∠DCB + ∠CBA
360 ° = 49 ° + 49 ° + ∠DCB + ∠CBA
∠DCB + ∠CBA = 262 °
∠DCB = ∠CBA (by the property of an isosceles trapezoid).
Then ∠DCB = ∠CBA = 262 ° / 2 = 131 °
Answer: ∠DCB = ∠CBA = 131 °, ∠BAD = ∠ADC = 49
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