Draw an angle of measure `135 ^(@) ` and bisect it.

Answer

To solve the problem of drawing an angle of measure 135 degrees and then bisecting it, follow these steps:

### Step-by-Step Solution:

1. **Draw a Base Line**:
- Start by drawing a horizontal line using a ruler. This will serve as one side of the angle.

**Hint**: Use a ruler to ensure the line is straight and long enough for your angle.

2. **Mark the Vertex**:
- Choose a point on the line to be the vertex of the angle. Label this point as O.

**Hint**: Make sure the point is clearly marked so you can easily refer to it later.

3. **Construct the Angle**:
- Using a protractor, place the center hole of the protractor at point O.
- Measure 135 degrees from the base line and mark this point. Label it as point A.

**Hint**: Ensure the protractor is aligned properly with the base line for accurate measurement.

4. **Draw the Angle**:
- Draw a line from point O to point A. This line represents one side of the angle.

**Hint**: Use a ruler to make the line straight and extend it sufficiently.

5. **Label the Angle**:
- Now, from point O, draw another line that forms the angle with point A. Label this point as B.

**Hint**: Ensure that the angle AOB is clearly visible and labeled.

6. **Draw an Arc**:
- With the compass, place the pointer on point O and draw an arc that intersects both sides of the angle (OA and OB). Label the intersection points as M and N.

**Hint**: Keep the compass width consistent while drawing the arc to ensure accuracy.

7. **Construct the Bisector**:
- Now, with the compass, place the pointer on point M and draw an arc above and below the angle.
- Without changing the compass width, place the pointer on point N and draw another arc that intersects the first two arcs. Label the intersection points as P.

**Hint**: Make sure the arcs intersect clearly so you can easily find the bisector.

8. **Draw the Bisector**:
- Finally, use a ruler to draw a straight line from point O through point P. This line OP is the bisector of angle AOB.

**Hint**: Ensure that the line is straight and extends sufficiently to show the bisector clearly.

### Conclusion:
You have successfully drawn an angle of 135 degrees and bisected it. The angle AOB is now divided into two equal parts by the line OP.