Answer:
A
Step-by-step explanation:
The Tangent-Secant Exterior Angle Measure Theorem states that if a tangent and a secant or two tangents/secants intersect outside of a circle, then the measure of the angle formed by them is half of the difference of the measures of its intercepted arcs. Basically, what that means here is that [tex]x[/tex] equals half of the difference of [tex]30\textdegree[/tex] and the measure of the unlabeled arc.
First, we need to find the measure of the unlabeled arc, since we can't find [tex]x[/tex] without it. We know that the measure of the full arc formed by the circle is [tex]360\textdegree[/tex], so the measure of the unlabeled arc must be [tex]360-30-100-100=130\textdegree[/tex] by the Arc Addition Postulate.
Now, we can find [tex]x[/tex]. Using all of the information known, we can solve for [tex]x[/tex] like this:
[tex]\\x=\frac{1}{2} (130\textdegree-30\textdegree)\\=\frac{1}{2} (100\textdegree)\\=50\textdegree[/tex]
Hope this helps!
