Question

which statements are true? check all that apply
□ (mwidehat{cb}=120^{circ})
□ (mwidehat{cb}=60^{circ})
□ (mangle cob = 2(mangle cab))
□ (mangle cob = 120^{circ})
□ (mangle cob=\frac{1}{2}(mangle cab))

Explanation:

Step1: Recall central - inscribed angle relationship

The measure of an arc is equal to the measure of the central angle that subtends it. The measure of an inscribed angle is half of the measure of the central angle that subtends the same arc. Given $\angle CAB = 60^{\circ}$, and $\angle COB$ is the central angle and $\angle CAB$ is the inscribed angle subtending arc $\overset{\frown}{CB}$.

Step2: Calculate the measure of arc $\overset{\frown}{CB}$ and $\angle COB$

By the inscribed - angle theorem, $m\angle COB=2m\angle CAB$. Since $m\angle CAB = 60^{\circ}$, then $m\angle COB = 120^{\circ}$. Also, the measure of arc $\overset{\frown}{CB}$ is equal to the measure of the central angle that subtends it, so $m\overset{\frown}{CB}=120^{\circ}$.

Answer:

$m\overset{\frown}{CB}=120^{\circ}$, $m\angle COB = 2(m\angle CAB)$, $m\angle COB = 120^{\circ}$