Answer:
[tex]\displaystyle \angle A=30^\circ[/tex]
Step-by-step explanation:
We are given that in Circle O, Arc BAC measures 300°.
Recall that arc lengths will always total 360°. Therefore:
[tex]\stackrel{\frown}{BAC}+\stackrel{\frown}{CB}=360^\circ[/tex]
By substitution:
[tex]300+\stackrel{\frown}{CB}=360[/tex]
Thus:
[tex]\stackrel{\frown}{CB}=60^\circ[/tex]
∠A intercepts Arc CB. Since it is an inscribed angle, it will be half of its intercepted arc. In other words:
[tex]\angle A=\displaystyle \frac{1}{2}\stackrel{\frown}{CB}[/tex]
Therefore:
[tex]\displaystyle \angle A=\frac{1}{2}(60)=30^\circ[/tex]
