Given below are the steps of construction to construct a quadrilateral KLMN where KL = 6 cm, LM = 8 cm, MN = 9.5 cm, `angleL = 105^(@) and angleM = 75^(@)`. Which of the following steps is incorrect?
Step-1 : Draw LM=8 cm and construct `angleMLX=105^(@)`.
Step-2 : With L as centre and radius 6 cm, draw an arc which cuts LX at K.
Step-3 : Construct `angleLMY = 75^(@)`. With M as centre and radius 9.5 cm, draw an are which cuts MY at N.
Step-4 : Now join N and X to obtain the required quadrilateral KLMN.

Options

A. Step-3
B. Step-1
C. Step-2
D. Step-4

Answer

To determine which step is incorrect in the construction of quadrilateral KLMN, let's analyze each step systematically.

### Step-by-Step Solution:

**Step 1: Draw LM = 8 cm and construct angle MLX = 105°**
- Start by drawing a line segment LM that measures 8 cm.
- At point L, construct an angle MLX of 105°.
- This step is correct as it establishes one side and an angle of the quadrilateral.

**Step 2: With L as center and radius 6 cm, draw an arc which cuts LX at K.**
- From point L, use a compass to measure a radius of 6 cm and draw an arc that intersects line LX at point K.
- This step is also correct as it places point K at the correct distance from L.

**Step 3: Construct angle LMY = 75°. With M as center and radius 9.5 cm, draw an arc which cuts MY at N.**
- At point M, construct an angle LMY of 75°.
- Then, using M as the center, draw an arc with a radius of 9.5 cm that intersects line MY at point N.
- This step is correct as it establishes another angle and distance in the quadrilateral.

**Step 4: Now join N and X to obtain the required quadrilateral KLMN.**
- This step states to join points N and X.
- However, the correct procedure should be to join points N and K, as K is the point we found in Step 2 that is connected to L.
- Therefore, this step is incorrect.

### Conclusion:
The incorrect step in the construction process is **Step 4**, which incorrectly instructs to join N and X instead of N and K.