Answer:
arc AD = 138°
Explanation:
Recall: if two inscribed angles are subtended by the same arc, the two angles are congruent or equal to each other based on the inscribed angle theorem.
<ABD and <ACD are two inscribed angles subtended by the same arc, therefore, they are equal.
Thus:
7x + 20 = 55 + 2x
Solve for x. Collect like terms
7x - 2x = 55 - 20
5x = 35
Divide both sides by 5
x = 35/5
x = 7
✔️m<ACD = ½(arc AD) (Inscribed angle theorems)
Substitute
55 + 2x = ½(arc AD)
Plug in the value of x
55 + 2(7) = ½(arc AD)
55 + 14 = ½(Arc AD)
69 = ½(Arc AD)
Multiply both sides by 2
2*69 = Arc AD
138° = arc AD
arc AD = 138°