PLEASE NEED HELP ON THE QUESTION (20 POINTS) THANK YOU :D

Question

asked Apr 10, 2019 211k views

2 Answers

Bvoleti · Answer 1 · 2019-04-15T22:08:45+0000

Let's start by knowing what information we are given in the problem and what we can infer.

We can see that
$\angle OAD$ is an central angle, meaning that
$m\angle OAD = m \stackrel \frown{AC}$ . Essentially, the measure of the central angle (
$\angle OAD$ ) is the same as the measure of the arc (
$\stackrel \frown{AC}$ ) of which it relates to. Since we figured out that
$\angle OAD = 62^(\circ)$ , we can also say
$m \stackrel \frown{AC} = 62^(\circ)$ .
$\angle ABC$ is an inscribed angle, meaning that
$m\angle ABC = (1)/(2) \,m\stackrel \frown{AC}$ . Essentially, the measure of
$\angle ABC$ is equal to one-half of the measure of
$\stackrel \frown{AC}$ .

Using this information, we can say that
$m \angle ABC = (1)/(2) (62^(\circ)) = 31^(\circ)$ . Thus,
$\boxed{m \angle ABC = 31^(\circ)}$