Construct the following quadrilaterals.
Quadrilateral
PLAN
PL=4cm
LA=6.5cm
`/_P=90^(@)`
`/_A=110^(@)`
`/_N=85^(@)`

Answer

To construct the quadrilateral PLAN with the given dimensions and angles, follow these steps:

### Step-by-Step Solution:

1. **Calculate Angle L**:
- Given angles: ∠P = 90°, ∠A = 110°, ∠N = 85°.
- Use the formula for the sum of angles in a quadrilateral:
\[ \text{Sum of angles} = 360° \]
- Calculate ∠L:
\[ \angle L = 360° - (90° + 110° + 85°) = 360° - 285° = 75° \]

2. **Draw Line Segment PL**:
- Using a ruler, draw a line segment PL = 4 cm.

3. **Construct Angle P (90°)**:
- At point P, use a protractor to construct a right angle (90°). Draw a line from P upwards; label this point as point A.

4. **Mark Point A**:
- From point P, measure 6.5 cm along the line you just drew (the vertical line). Mark this point as A.

5. **Construct Angle A (110°)**:
- At point A, use a protractor to measure and draw an angle of 110° from the line PA. This will create a new line extending from point A. Label the intersection of this line with the horizontal line as point N.

6. **Construct Angle N (85°)**:
- At point N, use a protractor to measure and draw an angle of 85° from the line AN. Extend this line until it intersects the line PL. Mark this intersection as point L.

7. **Complete the Quadrilateral**:
- Connect points L and N to complete the quadrilateral PLAN.

### Final Check:
- Ensure that the lengths PL = 4 cm, LA = 6.5 cm, and the angles ∠P = 90°, ∠A = 110°, ∠N = 85°, and ∠L = 75° are accurately represented.