If `bar (BX)` bisects `angle ABC` of measure `75^(@),` what will be the measure of `angle ABX?`

Options

A. `75^(@)`
B. `(37 (1)/(2)) ^(@)`
C. `15 0^(@)`
D. `(25 (1)/(2)) ^(@)`

Answer

To find the measure of angle ABX when line BX bisects angle ABC, follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We know that angle ABC measures 75 degrees.
- BX is the line that bisects angle ABC.

2. **Understand the Concept of Bisecting an Angle**:
- When an angle is bisected, it is divided into two equal parts. This means that angle ABX and angle XBC are equal.

3. **Calculate the Measure of Angle ABX**:
- Since BX bisects angle ABC, we can find the measure of angle ABX by dividing the total measure of angle ABC by 2.
- Therefore, angle ABX = (Measure of angle ABC) / 2 = 75 degrees / 2.

4. **Perform the Division**:
- 75 degrees divided by 2 equals 37.5 degrees.

5. **Conclusion**:
- The measure of angle ABX is 37.5 degrees.

### Final Answer:
- The measure of angle ABX is **37.5 degrees**.