#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

## Chapter 16: Understanding Shapes-II (Quadrilaterals)

### RD Sharma solutions for Class 8 Maths Chapter 16 Understanding Shapes-II (Quadrilaterals) Exercise 16.1 [Pages 15 - 17]

Define the following term Quadrilateral .

Define the following term Convex Quadrilateral .

In a quadrilateral, define of the following Sides.

In a quadrilateral, define of the following Vertices .

In a quadrilateral, define of the following Angles .

In a quadrilateral, define of the following Diagonals .

In a quadrilateral, define of the following Adjacent angles .

In a quadrilateral, define of the following Adjacent sides .

In a quadrilateral, define of the following Opposite sides .

In a quadrilateral, define of the following Opposite angles .

In a quadrilateral, define of the following Interior .

In a quadrilateral, define of the following Exterior .

Complete of the following, so as to make a true statement:

A quadrilateral has ....... sides.

Complete of the following, so as to make a true statement:

A quadrilateral has ...... angles.

Complete of the following, so as to make a true statement:

A quadrilateral has ..... vertices, no three of which are .....

Complete of the following, so as to make a true statement:

A quadrilateral has .... diagonals.

Complete of the following, so as to make a true statement:

The number of pairs of adjacent angles of a quadrilateral is .......

Complete of the following, so as to make a true statement:

The number of pairs of opposite angles of a quadrilateral is .......

Complete of the following, so as to make a true statement:

The sum of the angles of a quadrilateral is ......

Complete of the following, so as to make a true statement:

A diagonal of a quadrilateral is a line segment that joins two ...... vertices of the quadrilateral.

Complete of the following, so as to make a true statement:

The sum of the angles of a quiadrilateral is .... right angles.

Complete of the following, so as to make a true statement:

The measure of each angle of a convex quadrilateral is ..... 180°.

Complete of the following, so as to make a true statement:

In a quadrilateral the point of intersection of the diagonals lies in .... of the quadrilateral.

Complete of the following, so as to make a true statement:

A point is in the interior of a convex quadrilateral, if it is in the ..... of its two opposite angles.

**Complete of the following, so as to make a true statement:**

A quadrilateral is convex if, for each side, the remaining ______ lie on the same side of the line containing the side.

In Fig. 16.19, *ABCD* is a quadrilateral.

Name a pair of adjacent sides.

In Fig. 16.19, *ABCD* is a quadrilateral.

Name a pair of opposite sides.

In Fig. 16.19, *ABCD* is a quadrilateral.

How many pairs of adjacent sides are there?

In Fig. 16.19, *ABCD* is a quadrilateral.

How many pairs of opposite sides are there?

In Fig. 16.19, *ABCD* is a quadrilateral.

Name a pair of adjacent angles.

In Fig. 16.19, *ABCD* is a quadrilateral.

Name a pair of opposite angles.

In Fig. 16.19, *ABCD* is a quadrilateral.

How many pairs of adjacent angles are there?

In Fig. 16.19, *ABCD* is a quadrilateral.

How many pairs of opposite angles are there?

The angles of a quadrilateral are 110°, 72°, 55° and *x*°. Find the value of *x*.

The three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.

A quadrilateral has three acute angles each measures 80°. What is the measure of the fourth angle?

A quadrilateral has all its four angles of the same measure. What is the measure of each?

Two angles of a quadrilateral are of measure 65° and the other two angles are equal. What is the measure of each of these two angles?

Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.

The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.

If the sum of the two angles of a quadrilateral is 180°. What is the sum of the remaining two angles?

In Fig. 16.20, find the measure of *∠MPN*.

The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?

In Fig. 16.21, the bisectors of *∠A* and *∠B* meet at a point *P*. If *∠C* = 100° and *∠D* = 50°, find the measure of *∠APB*.

In a quadrilateral *ABCD*, the angles *A, B, C* and *D* are in the ratio 1 : 2 : 4 : 5. Find the measure of each angle of the quadrilateral.

In a quadrilateral *ABCD, CO* and *DO* are the bisectors of *∠C* and *∠D* respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]

Find the number of side of a regular polygon, when of its angle has a measure of 160° .

Find the number of side of a regular polygon, when of its angle has a measure of 135° .

Find the number of side of a regular polygon, when of its angle has a measure of 175° .

Find the number of side of a regular polygon, when of its angle has a measure of 162° .

Find the number of side of a regular polygon, when of its angle has a measure of 150° .

Find the number of degrees in each exterior exterior angle of a regular pentagon.

The measure of angles of a hexagon are *x*°, (*x* − 5)°, (*x* − 5)°, (2*x* − 5)°, (2*x* − 5)°, (2*x* + 20)°. Find the value of *x*.

In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.

*PQRSTU* is a regular hexagon. Determine each angle of Δ*PQT*.

## Chapter 16: Understanding Shapes-II (Quadrilaterals)

## RD Sharma solutions for Class 8 Maths chapter 16 - Understanding Shapes-II (Quadrilaterals)

RD Sharma solutions for Class 8 Maths chapter 16 (Understanding Shapes-II (Quadrilaterals)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 8 Maths solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Maths chapter 16 Understanding Shapes-II (Quadrilaterals) are Properties of Trapezium, Angle Sum Property of a Quadrilateral, Properties of Kite, Classification of Polygons, Properties of a Parallelogram, Concept of Curves, Different Types of Curves - Closed Curve, Open Curve, Simple Curve., Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal, Interior Angles of a Polygon, Exterior Angles of a Polygon and Its Property, Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles, Property: The diagonals of a rhombus are perpendicular bisectors of one another., Properties of Rhombus, Property: The Opposite Sides of a Parallelogram Are of Equal Length., Property: The Opposite Angles of a Parallelogram Are of Equal Measure., Property: The adjacent angles in a parallelogram are supplementary., Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection), Property: The Diagonals of a Rectangle Are of Equal Length., Properties of Rectangle, Properties of a Square, Property: The diagonals of a square are perpendicular bisectors of each other..

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