Question

the measure of angle ABX is 4x-16 and the measure of CBX is 2x+6 what is x and then find the measure of angle ABC

Answer 1

The values of x and angle ABC are;

`\begin{gathered} x=11 \\ \measuredangle ABC=56^0 \end{gathered}`

Step-by-step explanation:

From the instruction above;

Line BX bisects angle ABC.

So;

`\measuredangle ABX=\measuredangle CBX`

Given;

`\begin{gathered} \measuredangle ABX=4x-16 \\ \measuredangle CBX=2x+6 \end{gathered}`

Substituting this values, we have;

`\begin{gathered} \measuredangle ABX=\measuredangle CBX \\ 4x-16=2x+6 \end{gathered}`

Then we can solve for x; collecting the like terms

`\begin{gathered} 4x-2x=6+16 \\ 2x=22 \\ x=(22)/(2) \\ x=11 \end{gathered}`

Then we can now solve for angle ABC;

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

`\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}`

Therefore, the values of x and angle ABC are;

`\begin{gathered} x=11 \\ \measuredangle ABC=56^0 \end{gathered}`