# 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 154o

Let the measure of its supplement be xo.

Then,

= x + 1540 = 1800

= x = 180o – 1540

= x = 260

Hence, the supplement of the given angle measures  930.

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 = 45o

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:-

1. 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 45o 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

= p + q > 450 + q

= 900 > 450 + q

= 900 – 450 > q

= q < 450

Hence , its complementary angle is less than 450.

(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

(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