R d sharma solutions mathematics class 8 Solutions for Chapter 16 understanding shapes quadrilaterals

Exercises in Chapter 16 understanding shapes quadrilaterals Grade 8

Understanding Shapes Quadrilaterals Exercise 16.1

Questions in Understanding Shapes Quadrilaterals Exercise 16.1

Define the following terms:

(i)Quadrilateral

(ii)Convex Quadrilateral

In a quadrilateral, define each of the following:

(i)Sides

(ii)Vertices

(iii)Angles

(iv)Diagonals

(v)Adjacent angles

(vi)Adjacent sides

(vii)Opposite sides

(viii)Opposite angles

(ix)Interior

(x)Exterior

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

(i)A quadrilateral hassides.

(ii)A quadrilateral hasangles.

(iii)A quadrilateral has, no three of which are .

(iv)A quadrilateral hasdiagonals.

(v)The number of pairs of adjacent angles of a quadrilateral is.

(vi)The number of pairs of opposite angles of a quadrilateral is.

(vii)The sum of the angles of a quadrilateral is.

(viii)A diagonal of a quadrilateral is a line segment that joins twovertices of the quadrilateral.

(ix)The sum of the angles of a quadrilateral isright angles.

(x)The measure of each angle of a convex quadrilateral is180°.

(xi)In a quadrilateral the point of intersection of the diagonals lies inof the quadrilateral.

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

(xiii)A quadrilateral is convex if for each side, the remaininglie on the same side of the line containing the side.

In Fig. ABCD is a quadrilateral.

(i)Name a pair of adjacent sides.

(ii)Name a pair of opposite sides.

(iii)How many pairs of adjacent sides are there?

(iv)How many pairs of opposite sides are there?

(v)Name a pair of adjacent angles.

(vi)Name a pair of opposite angles.

(vii)How many pairs of adjacent angles are there?

(viii)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 areequal. 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 Figure, find the measure of ∠MPN.

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

In Figure, 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 = 1/2 (∠A +∠B).

Find the number of sides of a regular polygon, when each of its angles has a measure of

(i) 160°

(ii) 135°

(iii) 175°

(iv)162°

(v) 150°

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

The measure of angles of a hexagon are x°, (x-5)°, (x-5)°, (2x-5)°, (2x-5)°, (2x+20)°. Find 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 sides 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 ΔPQT.

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Chapters in this book

Rational Numbers

Powers

Squares and Square Roots

Cube and Cube Roots

Playing with Numbers

Algebraic Expressions and Identities

Factorization

Division of Algebraic Expressions

Linear Equation in One Variable

Direct and Inverse Variations

Time and Work

Percentage

Profit Loss Discount and Value Added Tax

Compound Interest

Understanding Shapes Polygons

Understanding Shapes Quadrilaterals

Understanding Shapes Special Types Quadrilaterals

Practical Goemetry

Visualising Shapes

Area of Trapezium and Polygon

Volume Surface Area Cuboid Cube

Surface Area and Volume of Right Circular Cylinder

Classification And Tabulation Of Data

Classification And Tabulation Of Data Graphical Representation Of Data As Histograms

Pictorial Representation Of Data As Pie Charts Or Circle Graphs

Data Handling Probability

Introduction To Graphs