in the diagram of circle o, what is the measure of ∠abc? 30° 40° 50° 60°
in the diagram of circle o, what is the measure of ∠abc? 30° 40° 50° 60°
Answer
Answer:
30°
Explanation:
Step1: Recall the formula
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 $m\overset{\frown}{AC_{1}} = 210^{\circ}$ and the smaller arc be $m\overset{\frown}{AC_{2}}=150^{\circ}$.
Step2: Calculate the difference of arcs
The difference of the measures of the intercepted arcs is $210 - 150=60^{\circ}$.
Step3: Find the measure of the angle
By the formula $\angle ABC=\frac{1}{2}(m\overset{\frown}{AC_{1}}-m\overset{\frown}{AC_{2}})$, substituting the values we get $\angle ABC=\frac{1}{2}(210 - 150)=\frac{1}{2}\times60 = 30^{\circ}$.