Attempt this question on graph paper.
Write down :
the measure of angle ABB'

Answer

To solve the question of finding the measure of angle ABB' on a graph paper, let's follow these steps:

### Step-by-Step Solution:

1. **Assume Points A and B**:
Let's assume point A has coordinates (1, 2) and point B has coordinates (2, 3).

2. **Determine Point B'**:
Since B' is the reflection of point B across the x-axis, we can find the coordinates of B' by changing the sign of the y-coordinate of B.
- The coordinates of B are (2, 3), so the coordinates of B' will be (2, -3).

3. **Plot Points on Graph Paper**:
- Plot point A at (1, 2).
- Plot point B at (2, 3).
- Plot point B' at (2, -3).

4. **Draw Lines**:
- Draw a line segment from A to B.
- Draw a line segment from A to B'.
- You should now have two lines: AB and AB'.

5. **Identify Angle ABB'**:
- The angle ABB' is formed between the line segments AB and AB'.
- To find the measure of angle ABB', we can use the slopes of the lines.

6. **Calculate the Slopes**:
- The slope of line AB = (y2 - y1) / (x2 - x1) = (3 - 2) / (2 - 1) = 1.
- The slope of line AB' = (y2 - y1) / (x2 - x1) = (-3 - 2) / (2 - 1) = -5.

7. **Find the Angle Using the Tangent Formula**:
- The tangent of the angle θ between two lines with slopes m1 and m2 is given by:
\[ \tan(θ) = \frac{m1 - m2}{1 + m1 \cdot m2} \]
- Here, m1 = 1 and m2 = -5:
\[ \tan(θ) = \frac{1 - (-5)}{1 + (1)(-5)} = \frac{6}{1 - 5} = \frac{6}{-4} = -\frac{3}{2} \]

8. **Calculate the Angle**:
- To find the angle θ, we can use the arctan function:
\[ θ = \tan^{-1}(-\frac{3}{2}) \]
- This will give us an angle of approximately 45 degrees.

9. **Conclusion**:
- Therefore, the measure of angle ABB' is 45 degrees.