A circle is described around the trapezoid, one of whose angles is 49 °. Find the rest of the trapezoid angles

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