S.chand Class 8 Maths Solution Chapter 13 Parallelograms Exercise 13 A

 Exercise 13 A

Question 1

1. The measure of one angle of a parallelogram is $80^{\circ}$. What are the measures of the remaining angles ?

2. Two adjacent angles of a parallelogram are congruent. What is the measure of each?

3. Two adjacent sides of a parallelogram are $5 \mathrm{~cm}$ and $6 \mathrm{~cm}$ respectively. Find its perimeter.

4. Find each angle of a parallelogram if two consecutive angles are in the ratio $1: 3$.

5. The perimeter of a parallelogram is $180 \mathrm{~cm}$. One of its sides is greater than the other by $30 \mathrm{~cm}$. Find the length of the sides of the parallelogram.

6. Find the sizes of the angles of a parallelogram if one angle is $20^{\circ}$ less than twice the smallest angle.

7. $A B C D$ is a parallelogram. Find $x, y$ and $z$.

8. In the figure, find the four angles $A, B, C$ and $D$ of the parallelogram $A B C D$.

9. $A B C D$ is a parallelogram. $C E$ bisects $\angle C$ and $\mathrm{AF}$ bisects $\angle A$. In each of the following, if the statement is true, give a reason for the same.

(i) $\angle A=\angle C$

(ii) $\angle F A B=\frac{1}{2} \angle A$

(iii) $\angle D C E=\frac{1}{2} \angle C$.

(iv) $\angle F A B=\angle D C E$

(v) $\angle D C E=\angle C E B$

(vi) $\angle C E B=\angle F A B$

(vii) $C E \| A F$

(viii) $A E \| F C$.

Multiple Choice Questions (MCQs)

10. If the quadrilateral $\mathrm{ABCD}$ is a parallelogram. What is the value of $x$ ?

(a) $45^{\circ}$

(b) $30^{\circ}$

(c) $36^{\circ}$

(d) $37^{\circ}$

11. What values of a would make the given quadrilateral a parallelogram.

(a) $5 \frac{1}{4}$

(b) $5 \frac{1}{2}$

(c) $5 \frac{3}{4}$

(d) 5

High Order Thinking Skills (HOTS)

12. The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.

[Hint. Use Pythagoras theorem]

(a) $\sqrt{2}: 1$

(b) $2 \sqrt{2}: 1$

(c) $3: 2$

(d) $\sqrt{3}: 1$