Question

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

Answer 1

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 $m\angle ABC = \frac{1}{2} \,m\stackrel \frown{AC}$. 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 $m \angle ABC = \frac{1}{2} (62^{\circ}) = 31^{\circ}$. Thus, $\boxed{m \angle ABC = 31^{\circ}}$

Answer 2

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