Respuesta :

Answer:

The values of x and angle ABC are;

[tex]\begin{gathered} x=11 \\ \measuredangle ABC=56^0 \end{gathered}[/tex]

Explanation:

From the instruction above;

Line BX bisects angle ABC.

So;

[tex]\measuredangle ABX=\measuredangle CBX[/tex]

Given;

[tex]\begin{gathered} \measuredangle ABX=4x-16 \\ \measuredangle CBX=2x+6 \end{gathered}[/tex]

Substituting this values, we have;

[tex]\begin{gathered} \measuredangle ABX=\measuredangle CBX \\ 4x-16=2x+6 \end{gathered}[/tex]

Then we can solve for x; collecting the like terms

[tex]\begin{gathered} 4x-2x=6+16 \\ 2x=22 \\ x=\frac{22}{2} \\ x=11 \end{gathered}[/tex]

Then we can now solve for angle ABC;

Since line BX bisect angle ABC, Angle ABC equal 2 times angle ABX;

[tex]\begin{gathered} \measuredangle ABC=2(\measuredangle ABX) \\ \measuredangle ABC=2(4x-16) \\ \measuredangle ABC=8x-32 \\ \text{ since x=}11 \\ \measuredangle ABC=8(11)-32 \\ \measuredangle ABC=88-32 \\ \measuredangle ABC=56^0 \end{gathered}[/tex]

Therefore, the values of x and angle ABC are;

[tex]\begin{gathered} x=11 \\ \measuredangle ABC=56^0 \end{gathered}[/tex]

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