Question

AC = BD, mẠC = (5x + 5), mBC = (x + 16)® and mBD = (4x + 27).What is mBC?22°48°D11538°А

Answer 1

We are given two chords of equal length, this means that the arc they form are equal, this means:

$\text{mAC}=\text{mBD}$

Replacing the expressions for each arc we get:

$5x+5=4x+27$

From this expression we can solve for "x" first by subtracting "4x" to both sides:

$5x-4x+5=27$

Now we subtract 5 to both sides:

$5x-4x=27-5$

Now we add like terms:

$x=22$

Now we replace this value of "x" in the expression for arc BC-:

$\text{mBC}=x+16$

Replacing the value of "x":

$\begin{gathered} \text{mBC}=22+16 \\ \text{mBC}=38 \end{gathered}$