**NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.3 – Practical Geometry**

**NCERT Solutions for Class 8 Maths ****Chapter 4 Exercise 4.3 – Practical Geometry****, has been designed by the NCERT to test the knowledge of the student on the topic – Constructing a Quadrilateral – When two adjacent sides and three angles are known**

**1. Construct the following quadrilaterals**

**i. Quadrilateral MORE
MO = 6 cm
OR = 4.5 cm
∠M = 60°
∠O = 105°
∠R = 105°**

**Solution:**

**Steps of construction**

- Step 1. Draw the side MO = 6 cm
- Step 2. Draw ∠MOR = 105°, such that OR = 4.5 cm
- Step 3. Draw ∠OMX = 60° and ∠ORY = 105°
- Step 4. Mark the point of intersection of MX and RY as E

MORE is the required quadrilateral.

**ii. Quadrilateral PLAN
**

**PL = 4 cm**

**LA = 6.5 cm**

**∠P = 90°**

**∠A = 110°**

**∠N = 85°**

**Solution:**

In quadrilateral PLAN

∠P + ∠L + ∠A + ∠N = 360°

90° + ∠L + 110° + 85° = 360°

∠L = 75°

**Steps of construction**

- Step 1. Draw the side PL = 4 cm
- Step 2. Draw ∠PLA = 75°, such that LA = 6.5 cm
- Step 3. Draw ∠LAX = 110° and ∠LPY = 90°
- Step 4. Mark the point of intersection of AX and PY as N

PLAN is the required quadrilateral.

**iii. Parallelogram HEAR**

**HE = 5 cm
EA = 6 cm
∠R = 85°**

**Solution:**

∠E = ∠R = 85° (Opposite angles of a parallelogram are equal)

∠A + ∠R = 180° (Adjacent angles of a parallelogram are supplementary)

∠A + 85° = 180°

∠A = 95°

∠H = ∠A = 95° (Opposite angles of a parallelogram are equal)

**Steps of construction**

- Step 1. Draw the side HE = 4 cm
- Step 2. Draw ∠HEA = 85°, such that EA = 6 cm
- Step 3. Draw ∠EAX = 95° and ∠EHY = 95°
- Step 4. Mark the point of intersection of AX and HY as R

HEAR is the required parallelogram.

**iv. Rectangle OKAY**

**OK = 7 cm
KA = 5 cm**

**Solution:**

∠O = ∠K = ∠A = ∠Y = 90° (All angles of a rectangle are equal)

**Steps of construction**

- Step 1. Draw the side OK = 7 cm
- Step 2. Draw ∠OKA = 90°, such that KA = 5 cm
- Step 3. Draw ∠KAN = 90° and ∠KOM = 90°
- Step 4. Mark the point of intersection of AN and OM as Y

OKAY is the required rectangle.

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.4 – Practical Geometry can be accessed by clicking here**

**NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.3 – Practical Geometry**

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