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

PLEASE NEED HELP ON THE QUESTION (20 POINTS) THANK YOU :D-example-1
User LarrikJ
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2 Answers

1 vote
What the person below said very smart
User Pan Congwen
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2 votes

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

  1. 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).

  2. \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)}

User Bvoleti
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