Draw an angle of measure `45 ^(@)` and bisect it.

Answer

To solve the problem of drawing an angle of measure 45 degrees and then bisecting it, follow these steps:

### Step-by-Step Solution:

1. **Draw a Line Segment:**
- Start by drawing a horizontal line segment. This will be one side of the angle.
- Label the endpoints of the line segment as point O (the vertex of the angle) and point A (one endpoint of the line).

**Hint:** Use a ruler to ensure your line is straight.

2. **Measure and Mark 45 Degrees:**
- Using a protractor, place the center point of the protractor (the small hole) at point O.
- Align the baseline of the protractor with line OA.
- Find the 45-degree mark on the protractor and make a small mark above point O.

**Hint:** Make sure the protractor is properly aligned to get an accurate measurement.

3. **Draw the Second Line:**
- From point O, draw a straight line through the mark you made at the 45-degree angle. Label the point where this line intersects the mark as point B.

**Hint:** Use a ruler to connect point O to the mark accurately.

4. **Label the Angle:**
- You now have angle AOB, which measures 45 degrees.

**Hint:** You can write the angle notation as ∠AOB = 45°.

5. **Bisect the Angle:**
- To bisect the angle, place the compass point at point O and draw an arc that intersects both sides of the angle (line OA and line OB). Label the points where the arc intersects line OA and line OB as points M and N, respectively.

**Hint:** Ensure the compass is set to a comfortable width to draw the arc.

6. **Draw Arcs from Points M and N:**
- Without changing the compass width, place the compass point on point M and draw an arc above the angle.
- Now, place the compass point on point N and draw another arc that intersects the first arc you drew.

**Hint:** Make sure the compass width remains the same for both arcs.

7. **Label the Intersection Point:**
- Label the point where the two arcs intersect as point P.

**Hint:** This point P is crucial as it will help in bisecting the angle.

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

**Hint:** Ensure that the line is straight and extends sufficiently.

### Conclusion:
You have successfully drawn an angle of 45 degrees and bisected it, creating two angles of 22.5 degrees each.