Question

PLEASE HELP I DONT KNOW HOW TO SOLVE THIS :((​

Answer 1

Answer:

$\displaystyle \angle A=30^\circ$

Step-by-step explanation:

We are given that in Circle O, Arc BAC measures 300°.

Recall that arc lengths will always total 360°. Therefore:

$\stackrel{\frown}{BAC}+\stackrel{\frown}{CB}=360^\circ$

By substitution:

$300+\stackrel{\frown}{CB}=360$

Thus:

$\stackrel{\frown}{CB}=60^\circ$

∠A intercepts Arc CB. Since it is an inscribed angle, it will be half of its intercepted arc. In other words:

$\angle A=\displaystyle \frac{1}{2}\stackrel{\frown}{CB}$

Therefore:

$\displaystyle \angle A=\frac{1}{2}(60)=30^\circ$