## MP Board Class 7th Maths Solutions Chapter 5 Lines and Angles Ex 5.1

Question 1.

Find the complement of eachof the following angles:

Solution:

The sum of the measures of complementary angles is 90°.

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

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

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

Question 2.

Find the supplement of each of the following angles:

Solution:

The sum of measures of supplementary angles is 180°.

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

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

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

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:

The sum of the measures of complementary angles is 90° and that of supplementary angles is 180°.

(i) Sum of the measures of angles = 65° +115° = 180°

∴ These angles are supplementary angles.

(ii) Sum of the measures of angles = 63° + 27° = 90°

∴ These angles are complementary angles.

(iii) Sum of the measures of angles = 112° + 68° = 180°

∴ These angles are supplementary angles.

(iv) Sum of the measures of angles = 130° + 50° = 180°

∴ These angles are supplementary angles.

(v) Sum of the measures of angles = 45° + 45° = 90°

∴ These angles are complementary angles.

(vi) Sum of the measures of angles = 80°+ 10° =90°

∴ These angles are complementary angles.

Question 4.

Find the angle which is equal to its complement.

Solution:

Let the angle be x.

Complement of this angle is also x.

∵ The sum of the measures of a pair of complementary angles is 90°.

∴ x + x = 90° ⇒ 2x = 90°

Question 5.

Find the angle which is equal to its supplement.

Solution:

Let the angle be x.

Supplement of this angle is also x.

∵ The sum of the measures of a pair of supplementary angles is 180°.

∴ x + x = 180°

⇒ 2x = 180° ⇒ x = 90°

Question 6.

In the given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what changes should take place in ∠2 so that both the angles still remain supplementary.

Solution:

∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, then ∠2 should be increased by the same measure so that the given pair of angles remains supplementary.

Question 7.

Can two angles be supplementary if both of them are:

(i) acute?

(ii) obtuse?

(iii) right?

Solution:

(i) No. Acute angle is always less than 90°. It can be observed that two angles, even of 89°, cannot add up to 180°. Therefore, two acute angles cannot form a supplementary.

(ii) No. Obtuse angle is always greater than 90°. It can be observed that two angles, even of 91°, will always add up to more than 180°. Therefore, two obtuse angles cannot form a supplementary.

(iii) Yes. Right angles are of 90° and 90° + 90° = 180°.

Therefore, two right angles form a supplementary angle together.

Question 8.

An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

Solution:

Let A and B are two angles making a complementary angle pair and A is greater than 45°.

A + B = 90°

⇒ B = 90° – A

Therefore, B will be less than 45°.

Question 9.

In the adjoining figure:

(i) Is ∠1 adjacent to ∠2?

(ii) Is ∠AOC adjacent to ∠AOE?

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

(iv) Are ∠BOD and ∠DOA supplementary?

(v) Is ∠1 vertically opposite to ∠4?

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

Solution:

(i) Yes. Since, ∠1 and ∠2 have a common vertex O and a common arm OC. Also, their non-common arms OA and OE are on the opposite side of the common arm.

(ii) No. ∠AOC and ∠AOE have a common vertex O and also a common arm OA. But, their non-common arms OC and OE are on the same side of the common arm. Therefore, they are not adjacent to each other.

(iii) Yes. Since, ∠COE and ∠EOD have a common vertex O and a common arm OE. Also, their non-common arms, OC and OD, are opposite rays.

(iv) Yes. Since, ∠BOD and ∠DOA have a common vertex O and their non-common arms are opposite to each other.

(v) Yes. Since, ∠1 and ∠4 are formed due to the intersection of two straight lines, AB and CD.

(vi) ∠COB is the vertically opposite angle of ∠5 as they are formed due to the intersection of two straight lines, AB and CD.

Question 10.

Indicate which pairs of angles are:

(i) Vertically opposite angles.

(ii) Linear pairs.

Solution:

(i) ∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles as they are formed due to the intersection of two straight lines.

(ii) ∠1 and ∠5, ∠5 and ∠4 are forming linear pairs as they have a common vertex and also, have non-common arms opposite to each other.

Question 11.

In the following figure, is ∠1 adjacent to ∠2? Give reasons.

Solution:

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

Question 12.

Find the values of the angles x, y and z in each of the following:

Solution:

(i) Since, x and 55° are vertically opposite angles,

x = 55° .

x + y = 180° (Linear pair)

⇒ 55° + y = 180°

⇒ y = 180° – 55° = 125°

y = z (Vertically opposite angles)

∴ z = 125°

(ii) z = 40° (Vertically opposite angles)

y + z = 180° (Linear pair)

⇒ y = 180° – 40° = 140°

∵ 40° + x + 25° = 180°

(Angles on a straight line)

⇒ 65° + x = 180°

⇒ x = 180° – 65° = 115°

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 angles

Question 14.

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) ∠AOD, ∠BOC

(ii) ∠EOA, ∠AOB

(iii ) ∠EOB, ∠EOD

(iv) ∠EOA, ∠EOC

(v) ∠AOB and ∠AOE; ∠AOE and ∠EOD; ∠EOD and ∠DOC