Question

What is the value of x ??

Answer 1

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 $x$ equals half of the difference of $30\textdegree$ and the measure of the unlabeled arc.

First, we need to find the measure of the unlabeled arc, since we can't find $x$ without it. We know that the measure of the full arc formed by the circle is $360\textdegree$, so the measure of the unlabeled arc must be $360-30-100-100=130\textdegree$ by the Arc Addition Postulate.

Now, we can find $x$. Using all of the information known, we can solve for $x$ like this:

$\\x=\frac{1}{2} (130\textdegree-30\textdegree)\\=\frac{1}{2} (100\textdegree)\\=50\textdegree$

Hope this helps!