Question

find the value of unknown x in the following triangles p is q is 30 degrees r is x 7th class 5 th chapter exercise 3 ​

Answer 1

Answer:

1. Complementary angle = 90 −

given angle

(i) Complement of 20

= 90 20 70 − =

(ii) Complement of 63

= 90 63 27 − =

(iii) Complement of 57

= 90 57 33 − =

2. Supplementary angle = 180 −

given angle

(i) Supplement of 105

= 180 105 75 − =

(ii) Supplement of 87

= 180 87 93 − =

(iii) Supplement of 154

= 180 154 26 − =

3. If sum of two angles is 180

, then they are called supplementary angles.

If sum of two angles is 90 ,

then they are called complementary angles.

(i) 65 115 180 ° + ° = ° These are supplementary angles.

(ii) 63 27 90 ° + ° = ° These are complementary angles.

(iii) 112 68 180 ° + ° = ° These are supplementary angles.

(iv) 130 50 180 ° + ° = ° These are supplementary angles.

(v) 45 45 90 + = These are complementary angles.

(vi) 80 10 90 ° + ° = ° These are complementary angles.

4. Let one of the two equal complementary angles be x.

∴ x x + = 90

⇒ 2 90 x =

⇒

90 45

2

x = =

Thus, 45

is equal to its complement.

5. Let x be two equal angles of its supplement.

Therefore, x x + = ° 180 [Supplementary angles]

⇒ 2 180 x = °

⇒

180 90

2

x

°

= =

Thus, 90

is equal to its supplement.

6. I f∠ 1 is decreased then, ∠ 2 will increase with the same measure, so that both the angles still

remain supplementary.

7. (i) No, because sum of two acute angles is less than 180 . °

(ii) No, because sum of two obtuse angles is more than 180 . °

(iii) Yes, because sum of two right angles is 180 . °

8. Let the complementary angles be x and y, i.e., x y + = 90

It is given that x > 45

Adding y both sides, x y y + > + 45

⇒ 90 45 > + y

⇒ 90 45 − > y

⇒ y < 45

Thus, its complementary angle is less than 45 9. (i) Yes, in ∠ AOE, OC is common arm.

(ii) No, they have no non-common arms on opposite side of common arm.

(iii) Yes, they form linear pair.

(iv) Yes, they are supplementary.

(v) Yes, they are vertically opposite angles.

(vi) Vertically opposite angles of ∠ 5 is ∠ COB.

10. (i) Vertically opposite angles, ∠ 1, ∠ 4; ∠ 5, ∠ 2 + ∠ 3.

(ii) Linear pairs ∠ 1, ∠ 5; ∠ 5, ∠ 4.

11. ∠ 1 and ∠ 2 are not adjacent angles because their vertex is not common.

12. (i) x = ° 55 [Vertically opposite angles]

Now 55 180 ° + = ° y [Linear pair]

⇒ y = ° − ° = ° 180 55 125

Also y z = = ° 125 [Vertically opposite angles]

Thus, x y = ° = ° 55 , 125 and z = ° 125 .

(ii) 40 25 180 ° + + ° = ° x [Angles on straight line]

⇒ 65 180 ° + = ° x

⇒ x = ° − ° 180 65 = 115°

Now 40 180 ° + = ° y [Linear pair]

⇒ y = ° − ° = ° 180 40 140 ……….(i)

Also y z + = ° 180 [Linear pair]

⇒ 140 180 ° + = ° z [From eq. (i)]

⇒ z = ° − ° = ° 180 140 40

Thus, x y = ° = ° 115 , 140 and z = ° 40 .

13. (i) 90

(ii) 180° (iii) supplementary

(iv) linear pair (v) equal (vi) obtuse angles

14. (i) Obtuse vertically opposite angles means greater than 90

and equal ∠ AOD = ∠ BOC.

(ii) Adjacent complementary angles means angles have common vertex, common arm,

non-common arms are on either side of common arm and sum of angles is 90 .

(iii) Equal supplementary angles means sum of angles is 180° and supplement angles are

equal.

(iv) Unequal supplementary angles means sum of angles is 180° and supplement angles

are unequal.

i.e., ∠ AOE, ∠ EOC; ∠ AOD, ∠ DOC and ∠ AOB, ∠ BOC

(v) Adjacent angles that do not form a linear pair mean, angles have common ray but the

angles in a linear pair are not supplementary.

i.e., ∠ AOB, ∠ AOE; ∠ AOE, ∠ EOD and ∠ EOD, ∠ COD

Step-by-step explanation:

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