# NCERT Solution class 7 Mathematics EXERCISE- 5.1

# CHAPTER – 5

# EXERCISE – 5.1

**Q1.Find the complement of each of the following angles:**

**SOLUTION:-**

**(i) **Two angles are said to be complementary if the sum of their measures is 90^{0}

The given angle is 20^{0}

Let the measure of its complement be x^{0}.

Then,

= x + 20^{0} = 90^{0}

= x = 90^{0} – 20^{0}

= x = 70^{0}

Hence, THE COMPLEMENTE OF THE GIVEN ANGLE MEASURES 70^{0}

**(ii) **Two angles are said to be complementary if the sum of their measures is 90^{0}.

The given angle is 63^{0}

Let the measure of its complement be x^{0}

Then,

= x + 63^{0} = 90^{0}

= x

^{0}– 63

^{0}

= x = 27^{0}

Hence, the complement of the given angle measures 27^{0}.

**(iii) **Two angles are said to be complementary if the sum of their measures is 90^{0}

The given angle is 57^{0}

Let the measure of its complement be x^{0}.

Then,

= x + 57^{0}= 90^{0}

= x = 90^{0} – 57^{0}

= x = 33^{0}

Hence , the complement of the given angles measure 33^{0}.

**Q2. Find the supplement of each of the following angles**:

**SOLUTION:-**

**(i) ** Two angles are said to be supplementary if the sum of their measures is 180^{0}.

The given angle is 105^{0}.

Let the measure of its supplement be x^{0}

Then,

= x + 105^{0} = 180^{0}

= x = 180^{0} – 150^{0}

= x = 75^{0}

Hence , the supplement of the given angle measures 75^{0}.

**(ii) **Two angles are said to be supplementary if the sum of their measures is 180^{0}.

The given angle is 87^{0}.

Let the measures of its supplement be x^{0}.

Then,

= x + 87^{0 }= 180^{0}

= x = 180^{0} – 87^{0}

= x = 93^{0}

Hence, the supplement of the given angle measures 93^{0}.

**(iii) **Two angles are said to be supplementary if the sum of their measure is 180^{0}.

The given angle is 154^{o}

Let the measure of its supplement be x^{o}.

Then,

= x + 154^{0} = 180^{0}

= x = 180^{o} – 154^{0}

= x = 26^{0}

Hence, the supplement of the given angle measures 93^{0.}

**Q3. Identify which of the following pairs of angles are complementary and which are supplementary **

**(i) 65 ^{0 }, 115^{0}**

**SOLUTION:-**

We have to find the sum of given angles to identify whether the angles are complementary or supplementary

Then,

= 65^{0}+ 115^{0}

= 180^{0}

If the sum of two angle measure is 180^{0}, then the two angles are said to be supplementary .

These angles are supplementary angles.

**(ii) 63 ^{0 }, 27^{0}**

**SOLUTION:-**

We have to find the sum of given angles to identify whether the angles are complementary or supplementary

Then,

= 63^{0} + 27^{0}

= 90^{0}

This angle is complementary angle .

**(iii) 112 ^{0} , 68^{0}**

**SOLUTION:-**

112^{0} + 68^{0}

= 180^{0}

This angle is supplementary angles.

**(iv) 130 ^{0 }, 50^{0}**

**SOLUTION:-**

= 130^{0} + 50^{0}

= 180^{0}

This angle is supplementary angle

**(v) 45 ^{0} , 45^{0}**

**SOLUTION:-**

45^{0 }+ 45^{0}

= 90^{0}

This angle is complementary angle.

**(vi) 80 ^{0 }, 10^{0}**

**SOLUTION:-**

= 80^{0} + 10^{0}

^{ }= 90^{0}

This angle is complementary angles.

**Q4.** **Find the angle which equal to its complement.**

**SOLUTION:-**

Let the measure of the required angle angle be x^{0}

We know that, sum of measures of complementary angle pair is 90^{0}

Then,

= x + x = 90^{0}

= 2x = 90^{0}

= x = 90/2

= x = 45^{o}

Hence the required angle measures is 45^{0}.

**Q5.Find the angle which is equal to its supplement.**

**SOLUTION:-**

Let the measures of the required angle be x^{0}

We know that , sum of measures of supplementary angle pair is 180^{0}.

Then,

= x + x = 180^{0}

= 2x = 180^{0}

= x = 180/2

= x = 90^{0}

Hence the required angle measures is 90^{0}.

**Q6. In the given figure, Angle 1 , Angle 2 are supplementary angles **

**If Angle 1 is decreased , what changes should take place in Angle 2 so that both the angles still remain supplementary .**

**SOLUTION:-**

From the question, it is given that,

Angle 1 and Angle 2 are supplementary angles.

If Angle 1 is decreased, then Angle 2 must be increased by the same value. Hence, this angle pair remains , supplementary

**Q7. Can two angles be supplementary if both of them are:**

**(i) Acute?**

**SOLUTION:-**

No. If two angles are acute means less than 90^{0}, the two angles cannot be supplementary. Because , their sum will be always less than 90^{0}.

**(ii) Obtuse?**

**SOLUTION:-**

- If two angles are obtuse, means more than 90
^{0}, the two angles cannot be supplementary . Because , their sum will always more than 180^{0}.

**(iii) Right?**

**SOLUTION:-**

Yes. If two angles are right means both measures 90^{0}, then two angles can form a supplementary pair.

90^{0} + 90^{0} = 180^{0}.

**Q8.An angles is greater than 45 ^{0}.Is its complementary angle greater than 45^{0} or equal to 45^{o} or less than 45^{0}?**

**SOLUTION:-**

Let us assume the complementary angles be p and q,

We know that, sum of measures of complementary angle pair is 90^{0}

Then,

= p + q = 90^{0}

It is given in the question that p > 45^{0}

Adding q on both sides,

= p + q > 45^{0} + q

= 90^{0} > 45^{0} + q

= 90^{0} – 45^{0} > q

= q < 45^{0}

Hence , its complementary angle is less than 45^{0}.

**Q9. In the adjoining figure:**

**(i) Is Angle 1 adjacent to Angle 2 ?**

**SOLUTION:-**

By observing the figure we came to conclude that,

Yes, as Angle 1 and Angle 2 having a common vertex i.e. 0 and a common arm OC.

Their non – common arms OA and OE are on both the side of common arm.

**(ii) Is Angle AOC adjacent to Angle AOE?**

**SOLUTION:-**

By observing the figure , we came to conclude that,

No, since they are having a common vertex O and common arm OA.

But , they have no non- common arms on the both sides of the common arm.

**(iii) Do Angle COE and Angle EOD form a linear pair ?**

**SOLUTION:- **

By observing the figure , we came to conclude that,

Yes, as Angle COE and Angle EOD having a common vertex i.e. O and a common arm OE.

Their non – common arms OC and OD are on both side of common arm.

**(iv) Are Angle BOD and Angle DOA supplement?**

**SOLUTION:-**

By observing the figure, we came to conclude that,

Yes. as Angle BOD and Angle DOA having a common vertex i.e. O and a common arm OE.

Their non – common arms OA and OB are opposite to each other.

**(v) Is Angle 1 vertically opposite to Angle 4?**

**SOLUTION:-**

Yes. Angle 1 and Angle 2 are formed by the intersection of two straight lines AB and CD.

**(vi) What is the vertically opposite angle of Angle 5?**

**SOLUTION:-**

Angle COB is the vertically opposite angle of Angle 5.Because these two angles are formed by the intersection of two straight lines AB and CD.

**Q10. Indicate which pairs of angles are:**

**SOLUTION:-**

** **

** **

**(i) Vertically opposite angles.**

**Solution:-**

By observing the figure we can say that,

Angle 1 and Angle 4 , Angle 5 and Angle 2 + Angle 3 are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines.

**(ii) Linear pairs.**

**SOLUTION:-**

By observing the figure we can say that,

Angle 1 and Angle 5 , Angle 5 and Angl0e 4 as these are having a common vertex and also having non common arms to opposite to each other.

**Q11. In the following figure, is Angle 1 adjacent to Angle 2 ? Give reasons.**

**SOLUTION:-**

Angle 1 and Angle 2 are not adjacent angles. Because, they are not lie on the same vertex.

**Q 12. Find the values of the angles x,y and z in each of the following:**

**(i) **

**SOLUTION:-**

Angle x = 55^{0}, because vertically opposite angles.

Angle x + Angle y = 180^{0} [ linear pair]

= 55^{0} + Angle y = 180^{0}

= Angle y = 180^{0} – 55^{0}

= Angle y = 125^{0}

Then , Angle y = Angle Z [ vertically opposite angles]

Angle z = 125^{0}

**(ii) **Angle z = 40^{0} because vertically opposite angles.

Angle y + Angle z = 180^{0} [ linear pair]

= Angle y + 40^{0} = 180^{0}

= Angle y = 180^{0} – 40^{0}

= Angle y = 140^{0}

Then 40 + Angle x + 25 = 180^{0} [ angles on straight line]

65 + Angle x = 180^{0}

Angle x = 180^{0} – 65^{0}

Angle x = 115^{0}

**Q13. Fill in the blanks:**

**(i) If two angles are complementary , then the sum of their measure is _**90^{0}**____.**

**(ii) If two angles are supplementary , then the sum of their measure is ____**180^{0}**___.**

**(iii) Two angles forming a linear pair are __**supplementary**_____.**

**(iv) If two adjacent angles are supplementary , they form a __**linear pair**_____.**

**(v) If two lines intersect at a point, then the vertically opposite angles are always __**equal**____.**

**(vi) If two lines intersect at a point , and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _**obtuse angles**_____.**

**Q14. In the adjoining figure, name the following pairs of angles. **

**(i) Obtuse vertically opposite angles**

**(ii) Adjacent complementary angles**

**(iii) Equal supplementary angles**

**(iv) Unequal supplementary angles**

**(v) Adjacent angles that do not form a linear pair**

**SOLUTION:-**

**(i) **Angle AOD and Angle BOC are obtuse vertically angles

**(ii) **Angle EOA and AOB are adjacent complementary angles

**(iii) **Angle EOB and Angle EOD are the equal supplementary angles

**(iv) **Angle EOA and Angle EOC are the UNEQUAL SUPPLEMENTARY ANGLES.

**(v) **Angle AOB and Angle AOE , Angle AOE and Angle EOD . Angle EOD and Angle COD are the adjacent angles that do not form a linear pair

** **