what is the measure of angle cab in circle o? 24° 48° 72° 96°
what is the measure of angle cab in circle o? 24° 48° 72° 96°
Answer
Explanation:
Step1: Recall the inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
Step2: Identify the intercepted arc
The inscribed angle $\angle CAB$ intercepts arc $CB$. The central angle corresponding to arc $CB$ is $48^{\circ}$.
Step3: Calculate the measure of $\angle CAB$
By the inscribed - angle theorem, if the central angle of an arc is $\theta$ and the inscribed angle of the same arc is $\alpha$, then $\alpha=\frac{\theta}{2}$. Here, $\theta = 48^{\circ}$, so $\alpha=\frac{48^{\circ}}{2}=24^{\circ}$.
Answer:
$24^{\circ}$