**Chapter
5 Lines and Angles**

**Exercise 5.1**

Ex 5.1 Class 7 Maths

**Question 1.
Find the complement of each of the following angles:**

Solution:

(i) Complement of 20° = 90° – 20° = 70°

(ii) Complement of 63° = 90° – 63° = 27°

(iii) Complement of 57° = 90° – 57° = 33°

Solution:

(i) Complement of 20° = 90° – 20° = 70°

(ii) Complement of 63° = 90° – 63° = 27°

(iii) Complement of 57° = 90° – 57° = 33°

**Ex 5.1 Class 7 Maths **

**Question 2.
Find the supplement of each of the following angles:**

Solution:

(i) Supplement of 105° = 180° – 105° = 75°

(ii) Supplement of 87° = 180° – 87° = 93°

(iii) Supplement of 154° = 180° – 154° = 26°

Solution:

(i) Supplement of 105° = 180° – 105° = 75°

(ii) Supplement of 87° = 180° – 87° = 93°

(iii) Supplement of 154° = 180° – 154° = 26°

**Ex 5.1 Class 7 Maths **

**Question 3.
Identify which of the following pairs of angles are complementary and which are
supplementary?
(i) 65°, 115°
(ii) 63°, 27°
(iii) 112°, 68°
(iv) 130°, 50°
(v) 45°, 45°
(vi) 80°, 10°**

Solution:

(i) 65° (+) 115° = 180°

They are supplementary angles.

(ii) 63° (+) 27° = 90°

They are complementary angles.

(iii) 112° (+) 68° = 180°

They are supplementary angles.

(iv) 130° (+) 50° = 180°

They are supplementary angles.

(v) 45° (+) 45° = 90°

They are complementary angles.

(vi) 80° (+) 10° = 90°

They are complementary angles.

**Ex 5.1 Class 7 Maths **

**Question 4.
Find the angle which equal to its complement.**

Solution:

Let the required angle be x°.

its complement = (90 – x)°

Now, re = 90 – x **⇒**** x + x = 90
**

**⇒**

**2x = 90**

**∴**

**x =**
= 45°

Thus the required angles are 45°.

Thus the required angles are 45°.

**Ex 5.1 Class 7 Maths **

**Question 5.
Find the angle which is equal to its supplement.**

Solution:

Let the required angle be x°.

**∴**** it supplement = (180 – x)°
Now, x = 180 – x
**

**⇒**

**x + x = 180**

**⇒**

**2x = 180°**

**∴**

Thus, the required angle is 90°.

Thus, the required angle is 90°.

**Ex 5.1 Class 7 Maths **

**Question 6.
In the given figure, **

**∠**

**1 and**

**∠**

**2 are supplementary angles.**

If

If

**∠**

**1 is decreased, what changes should take place in**

**∠**

**2 so that both the angles still remain supplementary.**

Solution:

Solution:

**∠**

**1 +**

**∠**

**2 = 180° (given)**

If

If

**∠**

**1 is decreased by some degrees, then**

**∠**

**2 will also be increased by the same degree so that the two angles still remain supplementary.**

**Ex 5.1 Class 7 Maths **

**Question 7.
Can two angles be supplementary if both of them are:
(i) acute?
(ii) obtuse?
(iii) right?**

(ii) Since, acute angle < 90°

(ii) Since, acute angle < 90°

**∴**

**Acute angle + acute angle < 90° + 90° < 180° Thus, the two acute angles cannot be supplementary angles. (ii) Since, obtuse angle > 90°**

**∴**

**Obtuse angle + obtuse angle > 90° + 90° > 180°**

Thus, the two obtuse angles cannot be supplementary angles.

(iii) Since, right angle = 90°

Thus, the two obtuse angles cannot be supplementary angles.

(iii) Since, right angle = 90°

**∴**

**right angle + right angle = 90° + 90° = 180°**

Thus, two right angles are supplementary angles.

Thus, two right angles are supplementary angles.

**Ex 5.1 Class 7
Maths Question 8.
An angle is greater than 45°. Is its complementary angle greater than 45° or
equal to 45° or less than 45 °?**

Solution:

Given angle is greater than 45°

Let the given angle be x°.

**∴**** x > 45
Complement of x° = 90° – x° < 45° [ **

**∵**

**x > 45°]**

Thus the required angle is less than 45°.

Thus the required angle is less than 45°.

**Ex 5.1 Class 7 Maths **

**Question 9.
In the following figure:
(i) Is **

**∠**

**1 adjacent to**

**∠**

**2?**

(ii) Is

(ii) Is

**∠**

**AOC adjacent to**

**∠**

**AOE?**

(iii) Do

(iii) Do

**∠**

**COE and**

**∠**

**EOD form a linear pair?**

(iv) Are

(iv) Are

**∠**

**BOD and**

**∠**

**DOA supplementary?**

(v) Is

(v) Is

**∠**

**1 vertically opposite angle to**

**∠**

**4?**

(vi) What is the vertically opposite angle of

(vi) What is the vertically opposite angle of

**∠**

**5?**

Solution:

(i) Yes,

Solution:

(i) Yes,

**∠**

**1 and**

**∠**

**2 are adjacent angles.**

(ii) No,

(ii) No,

**∠**

**AOC is not adjacent to**

**∠**

**AOE. [**

**∵**

**OC and OE do not lie on either side of common arm OA] .**

(iii) Yes,

(iii) Yes,

**∠**

**COE and**

**∠**

**EOD form a linear pair of angles.**

(iv) Yes,

(iv) Yes,

**∠**

**BOD and**

**∠**

**DOA are supplementary. [**

**∵**

**∠**

**BOD +**

**∠**

**DOA = 180°]**

(v) Yes,

(v) Yes,

**∠**

**1 is vertically opposite to**

**∠**

**4.**

(vi) Vertically opposite angle of

(vi) Vertically opposite angle of

**∠**

**5 is**

**∠**

**2 +**

**∠**

**3 i.e.**

**∠**

**BOC.**

**Ex 5.1 Class 7 Maths **

**Question 10.
Indicate which pairs of angles are:
(i) Vertically opposite angles
(ii) Linear pairs**

Solution:

(i) Vertically opposite angles are

Solution:

(i) Vertically opposite angles are

**∠**

**1 and**

**∠**

**4,**

**∠**

**5 and (**

**∠**

**2 +**

**∠**

**3)**

(ii) Linear pairs are

(ii) Linear pairs are

**∠**

**1 and**

**∠**

**5,**

**∠**

**5 and**

**∠**

**4**

**Ex 5.1 Class 7 Maths **

**Question 11.
In the following figure, is **

**∠**

**1 adjacent to**

**∠**

**2? Give reasons.**

Solution:

No,

Solution:

No,

**∠**

**1 and**

**∠**

**2 are not adjacent angles.**

Reasons:

(i)

Reasons:

(i)

**∠**

**1 +**

**∠**

**2 ≠ 180°**

(ii) They have no common vertex.

(ii) They have no common vertex.

**Ex 5.1 Class 7 Maths **

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

Solution:

From Fig. 1. we have

Solution:

From Fig. 1. we have

**∠**

**x =**

**∠**

**55° (Vertically opposite angles)**

**∠**

**x +**

**∠**

**y = 180° (Adjacent angles)**

55° +

55° +

**∠**

**y = 180° (Linear pair angles)**

**∴**

**∠**

**y = 180° – 55° = 125°**

**∠**

**y =**

**∠**

**z (Vertically opposite angles)**

125° =

125° =

**∠**

**z**

Hence,

Hence,

**∠**

**x = 55°,**

**∠**

**y = 125° and**

**∠**

**z = 125°**

**(ii) 25° + x + 40° = 180° (Sum of adjacent angles on
straight line)
65° + x = 180°
**

**∴**

**x = 180° – 65° = 115°**

40° + y = 180° (Linear pairs)

40° + y = 180° (Linear pairs)

**∴**

**y = 180° – 40° = 140°**

y + z = 180° (Linear pairs)

140° + z = 180°

y + z = 180° (Linear pairs)

140° + z = 180°

**∴**

**z = 180° – 140° = 40°**

Hence, x – 115°, y = 140° and z – 40°

Hence, x – 115°, y = 140° and z – 40°

**Ex 5.1 Class 7 Maths **

**Question 13.
Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is ______ .
(ii) If two angles are supplementary, then the sum of their measures is ______
.
(iii) Two angles forming a linear pair are ______ .
(iv) If two adjacent angles are supplementary, they form a ______ .
(v) If two lines intersect at a point, then the vertically opposite angles are
always ______ .
(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
______ .**

Solution:

(i) 90°

(ii) 180°

(iii) Supplementary

(iv) Linear pair

(v) Equal

(vi) Obtuse angle

**Ex 5.1 Class 7 Maths **

**Question 14.
In the given 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 but do not form a linear pair.

(i) Obtuse vertically opposite angles.

(ii) Adjacent complementary angles.

(iii) Equal supplementary angles.

(iv) Unequal supplementary angles.

(v) Adjacent angles but do not form a linear pair.

Solution:

(i)

Solution:

(i)

**∠**

**BOC and**

**∠**

**AOD are obtuse vertically opposite angles.**

(ii)

(ii)

**∠**

**AOB and**

**∠**

**AOE are adjacent complementary angles.**

(iii)

(iii)

**∠**

**EOB and**

**∠**

**EOD are equal supplementary angles.**

(iv)

(iv)

**∠**

**EOA and**

**∠**

**EOC are unequal supplementary angles.**

(v)

(v)

**∠**

**AOB and**

**∠**

**AOE,**

**∠**

**AOE and**

**∠**

**EOD,**

**∠**

**EOD and**

**∠**

**COD are adjacent angles but do not form a linear pair.**

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