Answer:
[tex]x=20[/tex]
Step-by-step explanation:
Refer to the diagram below for letter names of points.
Using the theorem provided on the second image, we can conclude that [tex]m\angle AOC=2*m\angle ABC=2*100\textdegree = 200\textdegree[/tex]. Keep in mind that this is the reflex [tex]\angle AOC[/tex].
Because [tex]O \in DC[/tex], we know that [tex]DC[/tex] is a diameter by definition, which makes [tex]m\angle DOC = 180\textdegree[/tex].
Using the Angle Addition Postulate, we can write the following equation:
[tex]m\angle AOD+m\angle DOC=m\angle AOC[/tex]
Substituting the measures of each angle into the equation gives us:
[tex]x\textdegree + 180\textdegree = 200\textdegree[/tex]
Solving the equation for [tex]x[/tex] gives us:
[tex]x\textdegree + 180\textdegree = 200\textdegree[/tex]
[tex]x\textdegree + 180\textdegree - 180\textdegree = 200\textdegree - 180\textdegree[/tex] (Subtract [tex]180\textdegree[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]x\textdegree = 20\textdegree \rightarrow \bf x=20[/tex] (Simplify)
Remember that [tex]x=20[/tex], not [tex]20\textdegree[/tex] because the degree symbol was already given in the original expression. Hope this helps!
