Answer:
The measure of arc AD is 194°.
Step-by-step explanation:
Let as consider the complete question is "Aaron is standing at point C, watching his friends on a Ferris wheel. He knows that he is looking up at a 57° angle and the measure of BD is 80°. What is the measure of AD?"
Outside Angles Theorem: If a tangent and a secant intersect outside the circle, then the measure of the angle formed by them is 1/2 of the absolute difference of the measures of the intercepted arcs.
Using this theorem we get
[tex]\angle ACB=\frac{1}{2}(Arc(AD)-Arc(BD))[/tex]
[tex]57=\frac{1}{2}(Arc(AD)-80)[/tex]
Multiply both sides by 2.
[tex]114=Arc(AD)-80[/tex]
Add 80 on both sides.
[tex]114+80=Arc(AD)-80+80[/tex]
[tex]194=Arc(AD)[/tex]
Therefore, the measure of arc AD is 194°.
