Check the picture attached.
BCD is an inscribed angle, so the measure of the arc BD (intercepted by angle BCD), is twice the measure of BCD.
So m arc (BAD)=2*122°=244°.
Let m(DAB)=α degrees, then m arc(BCD) is 2α degrees.
m arc (BAD) + m arc(BCD) =360°
[or m major arc(BD) + m minor arc(BD) =360°]
so
244°+2α°=360°
2α°=360°-244°=116°
α°=116°/2=58°
Answer:
m(BAD)=58°
Remark: In any quadrilateral inscribed in a circle, the opposite angles are supplementary, that is, the sum of their measures is 180°.
so given the angle with measure 122°, and asked for the measure of the opposite angle, by this theorem, we could have justified that the measure of the angle asked is 180°- 122°=58°
Also, if we are given that 2 opposite angles of a quadrilateral are supplementary, than we can circumscribe a circle to this quadrilateral.
