Answer:
arc AD = 72°
Step-by-step explanation:
Consider the below figure attached with the question.
If two chords intersect each other inside the circle, then
[tex]\text{Angle inside}=\dfrac{1}{2}(\text{Sum of intercepted arcs})[/tex]
For the given figure,
[tex]\angle AED=\dfrac{1}{2}(Arc(AD)+Arc(CB))[/tex]
[tex]89=\dfrac{1}{2}(7x-19+5x+41)[/tex]
[tex]89=\dfrac{1}{2}(12x+22)[/tex]
[tex]89=6x+11[/tex]
[tex]89-11=6x[/tex]
[tex]78=6x[/tex]
[tex]13=x[/tex]
The value of x is 13.
[tex]Arc(AD)=7x-19=7(13)-19=91-19=72[/tex]
Therefore, the measure of arc AD is 72°.
