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 secants

The measure of an angle formed by two secants is half the positive - difference of the measures of the intercepted arcs. Let the larger arc be $m\overset{\frown}{AC}=210^{\circ}$ and the smaller arc be $m\overset{\frown}{AC}' = 150^{\circ}$. The formula for $\angle ABC$ is $\angle ABC=\frac{1}{2}(m\overset{\frown}{AC}-m\overset{\frown}{AC}')$.

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, multiply by $\frac{1}{2}$: $\frac{1}{2}\times60=30$.

Answer:

$30^{\circ}$