Question

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

Explanation:

Step1: Recall angle - outside - circle formula

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 $m\overset{\frown}{AC_{major}} = 210^{\circ}$ and the minor arc be $m\overset{\frown}{AC_{minor}}=150^{\circ}$.
The formula for $\angle ABC$ (where $AB$ and $BC$ are tangents) is $\angle ABC=\frac{1}{2}(m\overset{\frown}{AC_{major}} - m\overset{\frown}{AC_{minor}})$.

Step2: Calculate the measure of $\angle ABC$

Substitute the values of the arcs into the formula:
$\angle ABC=\frac{1}{2}(210 - 150)$.
First, calculate the difference inside the parentheses: $210-150 = 60$.
Then, $\frac{1}{2}\times60=30^{\circ}$.

Answer:

$30^{\circ}$