We want to find the measure of arc AD. We would need to find x first as this would guide us toward finding AD.
We know from a circle geometry theorem that;
I. Angles in the same segment are equal. In this case,
[tex]\angle ABD\approx\angle ACD[/tex]
Therefore, we can equate them, equating them we obtain;
[tex]\begin{gathered} 11x-3=8x+15 \\ 11x-8x=15+3 \\ 3x=18 \\ x=6 \end{gathered}[/tex]
We could use this to obtain the measures of angle ABD or ACD, obtaining one is enough as they are congruent, let us use [tex]\begin{gathered} \angle ABD=11x-3 \\ =11(6)-3_{} \\ =66-3 \\ =63^o \end{gathered}[/tex]We can therefore find the measure of angle AD, by using the circle geometry theorem;
ii. Angles subtended at the centre of a circle is twice that subtended at the circumference;
Thus;
[tex]\begin{gathered} \angle AED=2\angle ACD \\ \angle AED=2(63) \\ \angle AED=126^o \end{gathered}[/tex]
Therefore, the measure of arc AD is 126 degrees.
