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

AC BD MẠC 5x 5 MBC X 16 And MBD 4x 27What Is MBC2248D11538А class=

Sagot :

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

[tex]\text{mAC}=\text{mBD}[/tex]

Replacing the expressions for each arc we get:

[tex]5x+5=4x+27[/tex]

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

[tex]5x-4x+5=27[/tex]

Now we subtract 5 to both sides:

[tex]5x-4x=27-5[/tex]

Now we add like terms:

[tex]x=22[/tex]

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

[tex]\text{mBC}=x+16[/tex]

Replacing the value of "x":

[tex]\begin{gathered} \text{mBC}=22+16 \\ \text{mBC}=38 \end{gathered}[/tex]

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