Question

in the diagram below, $overline{ab}$ and $overline{bc}$ are tangent to $odot o$. which expression gives the measure of $angle abc$? a. $\frac{1}{2}(240^{circ}-120^{circ})$ b. $240^{circ}-120^{circ}$ c. $240^{circ}+120^{circ}$ d. $\frac{1}{2}(240^{circ}+120^{circ})$

Explanation:

Step1: Recall tangent - arc relationship

The measure of an angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The larger intercepted arc is $240^{\circ}$ and the smaller intercepted arc is $120^{\circ}$.

Step3: Apply the formula

The measure of $\angle ABC=\frac{1}{2}(240^{\circ}- 120^{\circ})$.

Answer:

A. $\frac{1}{2}(240^{\circ}-120^{\circ})$