#### Chapter 14 Quadrilaterals R.D. Sharma Solutions for Class 9th Exercise 14.2

**Exercise 14.2**

1. Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.

**Solution**

2. If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.

**Solution**

3. Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle.

**Solution**

4. The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm what is the measure of the shorter side?

**Solution**

5. In a parallelogram ABCD, ∠D = 135°, determine the measures of ∠A and ∠B.

**Solution**

6. ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D.

**Solution**

**Solution**

8. In Fig. 14.35,

*ABCD*is a parallelogram in which ∠

*DAB*= 75° and ∠

*DBC*= 60°. Compute ∠

*CDB*and ∠

*ADB*.

**Solution**

9. In figure 14.36, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

**Solution**

10. Which of the following statements are true (T) and which are false (F)?

(i) In a parallelogram, the diagonals are equal.

(ii) In a parallelogram, the diagonals bisect each other.

(iii) In a parallelogram, the diagonals intersect each other at right angles.

(iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

(v) If all the angles of a quadrilateral are equal, it is a parallelogram.

(vi) If three sides of a quadrilateral are equal, it is a parallelogram.

(vii) If three angles of a quadrilateral are equal, it is a parallelogram.

(viii) If all the sides of a quadrilateral are equal, it is a parallelogram.

**Solution**

(i) False

(ii) True

(iii) False

(iv) False

(v) True

(vi) False

(vii) False

(viii) True