BX⎯→⎯b x with right arrow abovebisects ∠ABCangle eh b c. m∠ABXm angle eh b x = 4x – 16 and m∠CBXm angle c b x = 2x + 6. Find m∠ABXm angle eh b x.

Question

A.
22º

B.
28º

C.
11º

D.
5º

Answer 1

When we are given that \(BX\) bisects \(\angle ABC\), it means that \(\angle ABX = \angle CBX\).

We are given the measures of these angles as follows:
\[
m(\angle ABX) = 4x - 16
\]
\[
m(\angle CBX) = 2x + 6
\]

Since \(BX\) bisects \(\angle ABC\), these two angles are equal:
\[
4x - 16 = 2x + 6
\]

Let's solve this equation for \(x\):

First, subtract \(2x\) from both sides of the equation:
\[
4x - 2x - 16 = 6
\]
\[
2x - 16 = 6
\]

Next, add 16 to both sides:
\[
2x - 16 + 16 = 6 + 16
\]
\[
2x = 22
\]

Now, divide by 2:
\[
x = 11
\]

Now that we have the value of \(x\), we can find the measure of \(\angle ABX\):
\[
m(\angle ABX) = 4x - 16
\]

Substitute \(x = 11\):
\[
m(\angle ABX) = 4(11) - 16
\]
\[
m(\angle ABX) = 44 - 16
\]
\[
m(\angle ABX) = 28
\]

Therefore, the measure of \(\angle ABX\) is \(28^\circ\).

The correct answer is:
B. 28º