Question

in the diagram of circle o, what is the measure of ∠abc? 30° 40° 50° 60°

Explanation:

Step1: Recall the formula for the measure of an angle formed by two tangents

The measure of an angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs.
Let the major - arc be $m\overset{\frown}{AC}=210^{\circ}$ and the minor - arc be $m\overset{\frown}{AC}=150^{\circ}$. The formula for $\angle ABC$ (where $AB$ and $BC$ are tangents) is $\angle ABC=\frac{1}{2}(m\overset{\text{major arc}}{AC}-m\overset{\text{minor arc}}{AC})$.

Step2: Calculate the measure of $\angle ABC$

Substitute the values of the major and minor arcs into the formula:
$\angle ABC=\frac{1}{2}(210 - 150)$
$=\frac{1}{2}\times60$
$ = 30^{\circ}$

Answer:

$30^{\circ}$