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
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.
A.
22º
B.
28º
C.
11º
D.
5º
1 answer