Question

Find X.
Use angle center circle page for reference.
Explain your answer.

Answer 1

`x=20`

Explanation:

Refer to the diagram below for letter names of points.

Using the theorem provided on the second image, we can conclude that
`m\angle AOC=2*m\angle ABC=2*100\textdegree = 200\textdegree`. Keep in mind that this is the reflex
`\angle AOC`.

Because
`O \in DC`, we know that
`DC` is a diameter by definition, which makes
`m\angle DOC = 180\textdegree`.

Using the Angle Addition Postulate, we can write the following equation:

`m\angle AOD+m\angle DOC=m\angle AOC`

Substituting the measures of each angle into the equation gives us:

`x\textdegree + 180\textdegree = 200\textdegree`

Solving the equation for
`x` gives us:

`x\textdegree + 180\textdegree = 200\textdegree`

`x\textdegree + 180\textdegree - 180\textdegree = 200\textdegree - 180\textdegree` (Subtract
`180\textdegree` from both sides of the equation to isolate
`x`)

`x\textdegree = 20\textdegree \rightarrow \bf x=20` (Simplify)

Remember that
`x=20`, not
`20\textdegree` because the degree symbol was already given in the original expression. Hope this helps!