Construct a triangle ABC such that AB = BC = 5 cm and `angle B = 120^(@)` by using ruler and compass only. Measure angle A and C

Answer

To construct triangle ABC with the given conditions, follow these steps:

### Step-by-Step Construction:

1. **Draw Line Segment AB:**
- Use a ruler to draw a line segment AB that measures 5 cm. Label the endpoints as A and B.
- **Hint:** Ensure the measurement is accurate by using the ruler properly.

2. **Extend Line from Point B:**
- Extend the line from point B in both directions. This will help in constructing the angle.
- **Hint:** You can lightly draw the line to avoid confusion later.

3. **Construct Angle B (120 degrees):**
- Place the compass point on B and draw a semicircle that intersects the extended line on both sides of B.
- Label the points where the semicircle intersects the extended line as D and E.
- **Hint:** Make sure the semicircle is drawn accurately to help in measuring the angle.

4. **Mark the Angle:**
- With the compass still on point B, adjust it to a suitable width and mark an arc that intersects the semicircle. Label this intersection point as F.
- Draw a line from B to F. This line represents the angle of 120 degrees.
- **Hint:** Ensure that the arc is drawn lightly so it can be easily erased later if needed.

5. **Construct Line Segment BC:**
- With the compass set to 5 cm, place the compass point on B and draw an arc that intersects the line BF. Label the intersection point as C.
- **Hint:** Double-check the compass measurement to ensure BC is exactly 5 cm.

6. **Complete the Triangle:**
- Draw line segments AC and BC to complete triangle ABC.
- **Hint:** Use a ruler to ensure the lines are straight and accurately connect the points.

7. **Measure Angles A and C:**
- Use a protractor to measure angle A and angle C.
- **Hint:** Align the protractor accurately with the vertex and the sides of the angles for precise measurement.

### Conclusion:
You have successfully constructed triangle ABC with AB = BC = 5 cm and angle B = 120 degrees. The measures of angles A and C should both be 30 degrees.