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 90⁰

The given angle is 20⁰

Let the measure of its complement be x⁰.

Then,

= x + 20⁰ = 90⁰

= x = 90⁰ – 20⁰

= x = 70⁰

Hence, THE COMPLEMENTE OF THE GIVEN ANGLE MEASURES 70⁰

(ii) Two angles are said to be complementary if the sum of their measures is 90⁰.

The given angle is 63⁰

Let the measure of its complement be x⁰

Then,

= x + 63⁰ = 90⁰

= x = 90⁰ – 63⁰

= x = 27⁰

Hence, the complement of the given angle measures 27⁰.

(iii) Two angles are said to be complementary if the sum of their measures is 90⁰

The given angle is 57⁰

Let the measure of its complement be x⁰.

Then,

= x + 57⁰= 90⁰

= x = 90⁰ – 57⁰

= x = 33⁰

Hence , the complement of the given angles measure 33⁰.

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 180⁰.

The given angle is 105⁰.

Let the measure of its supplement be x⁰

Then,

= x + 105⁰ = 180⁰

= x = 180⁰ – 150⁰

= x = 75⁰

Hence , the supplement of the given angle measures 75⁰.

(ii) Two angles are said to be supplementary if the sum of their measures is 180⁰.

The given angle is 87⁰.

Let the measures of its supplement be x⁰.

Then,

= x + 87⁰= 180⁰

= x = 180⁰ – 87⁰

= x = 93⁰

Hence, the supplement of the given angle measures 93⁰.

(iii) Two angles are said to be supplementary if the sum of their measure is 180⁰.

The given angle is 154^o

Let the measure of its supplement be x^o.

Then,

= x + 154⁰ = 180⁰

= x = 180^o – 154⁰

= x = 26⁰

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) 65⁰, 115⁰

SOLUTION:-

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

Then,

= 65⁰+ 115⁰

= 180⁰

If the sum of two angle measure is 180⁰, then the two angles are said to be supplementary .

These angles are supplementary angles.

(ii) 63⁰, 27⁰

SOLUTION:-

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

Then,

= 63⁰ + 27⁰

= 90⁰

This angle is complementary angle .

(iii) 112⁰ , 68⁰

SOLUTION:-

112⁰ + 68⁰

= 180⁰

This angle is supplementary angles.

(iv) 130⁰, 50⁰

SOLUTION:-

= 130⁰ + 50⁰

= 180⁰

This angle is supplementary angle

(v) 45⁰ , 45⁰

SOLUTION:-

45⁰+ 45⁰

= 90⁰

This angle is complementary angle.

(vi) 80⁰, 10⁰

SOLUTION:-

= 80⁰ + 10⁰

= 90⁰

This angle is complementary angles.

Q4. Find the angle which equal to its complement.

SOLUTION:-

Let the measure of the required angle angle be x⁰

We know that, sum of measures of complementary angle pair is 90⁰

Then,

= x + x = 90⁰

= 2x = 90⁰

= x = 90/2

= x = 45^o

Hence the required angle measures is 45⁰.

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

SOLUTION:-

Let the measures of the required angle be x⁰

We know that , sum of measures of supplementary angle pair is 180⁰.

Then,

= x + x = 180⁰

= 2x = 180⁰

= x = 180/2

= x = 90⁰

Hence the required angle measures is 90⁰.

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 90⁰, the two angles cannot be supplementary. Because , their sum will be always less than 90⁰.

(ii) Obtuse?

SOLUTION:-

If two angles are obtuse, means more than 90⁰, the two angles cannot be supplementary . Because , their sum will always more than 180⁰.

(iii) Right?

SOLUTION:-

Yes. If two angles are right means both measures 90⁰, then two angles can form a supplementary pair.

90⁰ + 90⁰ = 180⁰.

Q8.An angles is greater than 45⁰.Is its complementary angle greater than 45⁰ or equal to 45^o or less than 45⁰?

SOLUTION:-

Let us assume the complementary angles be p and q,

We know that, sum of measures of complementary angle pair is 90⁰

Then,

= p + q = 90⁰

It is given in the question that p > 45⁰

Adding q on both sides,

= p + q > 45⁰ + q

= 90⁰ > 45⁰ + q

= 90⁰ – 45⁰ > q

= q < 45⁰

Hence , its complementary angle is less than 45⁰.

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 = 55⁰, because vertically opposite angles.

Angle x + Angle y = 180⁰ [ linear pair]

= 55⁰ + Angle y = 180⁰

= Angle y = 180⁰ – 55⁰

= Angle y = 125⁰

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

Angle z = 125⁰

(ii) Angle z = 40⁰ because vertically opposite angles.

Angle y + Angle z = 180⁰ [ linear pair]

= Angle y + 40⁰ = 180⁰

= Angle y = 180⁰ – 40⁰

= Angle y = 140⁰

Then 40 + Angle x + 25 = 180⁰ [ angles on straight line]

65 + Angle x = 180⁰

Angle x = 180⁰ – 65⁰

Angle x = 115⁰

Q13. Fill in the blanks:

(i) If two angles are complementary , then the sum of their measure is _90⁰____.

(ii) If two angles are supplementary , then the sum of their measure is ____180⁰___.

(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