Mathematics Class Eight   Class 8 Subject List

Solutions of NCERT Exercise

Number System
Exercise 1
Exercise 2
Linear Equations
Problem&Solution:Type1
Exercise 1
Exercise 2
   Part 1     Part 2     Part 3
Exercise 3
   Part 1     Part 2
Exercise 4
   Part 1     Part 2
Exercise 5
   Part 1     Part 2
Exercise 6
   Part 1     Part 2
Quadrilaterals
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Data Handling
Exercise 1
Exercise 2
Probability
Square & Square Roots
Exercise 1
Exercise 2
Exercise 3
   Part 1     Part 2
Exercise 4
Cube & Cube Roots
Exercise 1
Exercise 2
Comparing Quantities
Exercise 1
Exercise 2
Exercise 3
Algebraic Expressions
Exercise 1
Exercise 2 & 3
Exercise 4
Exercise 5
Exponents & Power
Factorization
Exercise 1
Exercise 2
Exercise 3
Mensuration
Mensuration:Problem:Type I
Mensuration:Problem:Type II
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Proportion
Exercise 1
Exercise 2
Introduction to Graphs
Exercise 1
Exercise 2 & 3
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Understanding Quadrilaterals

Exercise 3

1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.

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2. Consider the following parallelograms. Find the values of the unknowns x, y, z.

(i)

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(ii)

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Answer: x, y and z will be complementary to 50°.

So, Required angle = 180° - 50° = 130°

(iii)

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Answer: z being opposite angle= 80°

x and y are complementary, x and y

= 180° - 80° = 100°

(iv)

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Answer: As angles on one side of a line are always complementary

So, x = 90°

So, y = 180° - (90° + 30°) = 60°

The top vertex angle of the above figure = 60° x 2=120°

Hence, bottom vertex Angle = 120° and

z = 60°

(v)

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Answer: y= 112°, as opposite angles are equal in a parallelogram

x= 180°-(112°-40°)=28°

As adjacent angles are complementary so angle of the bottom left vertex

=180°-112°=68°

So, z=68°-40°=28°

Another way of solving this is as follows:

As angles x and z are alternate angles of a transversal so they are equal in measurement.

3. Can a quadrilateral ABCD be a parallelogram if

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Answer: (i)It can be , but not always as you need to look for other criteria as well.

(ii) In a parallelogram opposite sides are always equal, here AD BC, so its not a parallelogram.

(iii) Here opposite angles are not equal, so it is not a parallelogram.

5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

Answer: Opposite angles of a parallelogram are always add upto 180°.

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6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Answer: 90°, as they add up to 180°

7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

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Answer: Angle opposite to y = 180° - 70°=110°

Hence, y = 110°

x = 180° - (110° + 40°) = 30°, (triangle’s angle sum)

z = 30° (Alternate angle of a transversal)

8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

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Answer: As opposite sides are equal in a parallelogram

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Answer: As you know diagonals bisect each other in a parallelogram.

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9. In the given figure both RISK and CLUE are parallelograms. Find the value of x.

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Answer: In parallelogram RISK

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