Question

x =

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

Answer 1

$58^{\circ}$

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:

$m\angle CAE=\frac{1}{2}(mCE-mBD)$

Plugging into that the data we have:

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

And that's the answer