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21 votes
21 votes
X =

a) 43
b) 58
c) 71 I don’t understand how you got 58 I got 86

X = a) 43 b) 58 c) 71 I don’t understand how you got 58 I got 86-example-1
User Rommel
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1 Answer

6 votes
6 votes


58^(\circ)

1) In this problem, we can see two secant lines coming from the same point crossing that circle.

2) Thus, based on that we can write out the following relation to find the measure of arc x:

We can use this formula:


m\angle CAE=(1)/(2)(mCE-mBD)

Plugging into that the data we have:


\begin{gathered} m\angle28=(1)/(2)(114-x) \\ 28=(1)/(2)(114-x) \\ 28=57-(x)/(2) \\ -(x)/(2)+57=28 \\ -(x)/(2)+57-57=28-57 \\ -(x)/(2)=-29 \\ -2*(-(x)/(2))=-29*(-2) \\ x=58^(\circ) \\ \end{gathered}

And that's the answer

X = a) 43 b) 58 c) 71 I don’t understand how you got 58 I got 86-example-1
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