Exercise 5.1 (Revised) - Chapter 5 - Lines & Angles - Ncert Solutions class 7 - Maths

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Chapter 5 - Lines & Angles - NCERT Solutions for Class 7 Maths | Comprehensive Guide

Question 1.

Find the complement of each of the following angles: 

Answer:

Complementary angle $=90^{\circ}$ - given angle
(i) Complement of $20^{\circ}=90^{\circ}-20^{\circ}=70^{\circ}$
(ii) Complement of $63^{\circ}=90^{\circ}-63^{\circ}=27^{\circ}$
(iii) Complement of $57^{\circ}=90^{\circ}-57^{\circ}=33^{\circ}$

Ex 5.1 Question 2.

Find the supplement of each of the following angles:

Answer: Supplementary angle $=180^{\circ}$ - given angle
(i) Supplement of $105^{\circ}=180^{\circ}-105^{\circ}=75^{\circ}$
(ii) Supplement of $87^{\circ}=180^{\circ}-87^{\circ}=93^{\circ}$
(iii) Supplement of $154^{\circ}=180^{\circ}-154^{\circ}=26^{\circ}$

Ex 5.1 Question 3.

Identify which of the following pairs of angles are complementary and which are supplementary:

(i) $65^{\circ}, 115^{\circ}$
(ii) $63^{\circ}, 27^{\circ}$
(iii) $112^{\circ}, 68^{\circ}$
(iv) $130^{\circ}, 50^{\circ}$
(v) $45^{\circ}, 45^{\circ}$
(vi) $80^{\circ}, 10^{\circ}$

Answer:

If sum of two angles is $180^{\circ}$, then they are called supplementary angles.
If sum of two angles is $90^{\circ}$, then they are called complementary angles.
(i) $65^{\circ}+115^{\circ}=180^{\circ}$ These are supplementary angles.
(ii) $63^{\circ}+27^{\circ}=90^{\circ}$ These are complementary angles.
(iii) $112^{\circ}+68^{\circ}=180^{\circ}$ These are supplementary angles.
(iv) $130^{\circ}+50^{\circ}=180^{\circ}$ These are supplementary angles.
(v) $45^{\circ}+45^{\circ}=90^{\circ}$ These are complementary angles.
(vi) $80^{\circ}+10^{\circ}=90^{\circ}$ These are complementary angles.

Ex 5.1 Question 4.

Find the angle which is equal to its complement:

Answer:

Let one of the two equal complementary angles be $x$.
$
\begin{aligned}
& \therefore x+x=90^{\circ} \\
& \Rightarrow 2 x=90^{\circ} \\
& \Rightarrow \mathrm{x}=\frac{90^{\circ}}{2}=45^{\circ}
\end{aligned}
$

Thus, $45^{\circ}$ is equal to its complement.
Ex 5.1 Question 5.

Find the angle which is equal to its supplement.

Answer:

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

Therefore, $x+x=180^{\circ}$ [Supplementary angles]
$
\begin{aligned}
& \Rightarrow 2 x=180 \\
& \Rightarrow \mathrm{x}=\frac{180^{\circ}}{2}=90^{\circ}
\end{aligned}
$

Thus, $90^{\circ}$ is equal to its supplement.
Ex 5.1 Question 6.

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

Answer:

if $\angle 1$ is decreased then, $\angle 2$ will increase with the same measure, so that both the angles still remain supplementary.

Ex 5.1 Question 7.

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

Answer:

(i) No, because sum of two acute angles is less than $180^{\circ}$
(ii) No, because sum of two obtuse angles is more than $180^{\circ}$
(iii) Yes, because sum of two right angles is $180^{\circ}$

Ex 5.1 Question 8.

An angle is greater than $45^{\circ}$. Is its complementary angle greater than $45^{\circ}$ or equal to $45^{\circ}$ or less than $45^{\circ}$ ?

Answer:

Let the complementary angles be $x$ and $y$ i.e., $x+y=90^{\circ}$

It is given that $x>45^{\circ}$

Adding $y$ both sides, $x+y>45^{\circ}+y$
$
\begin{aligned}
& \Rightarrow 90^{\circ}>45^{\circ}+\mathrm{y} \\
& \Rightarrow 90^{\circ}-45^{\circ}>\mathrm{y} \\
& \Rightarrow \mathrm{y}<45^{\circ}
\end{aligned}
$

Thus, its complementary angle is less than $45^{\circ}$

Ex 5.1 Question 9.

Fill in the blanks:
1. If two angles are complementary, then the sum of their measures is _____________
2. If two angles are supplementary, then the sum of their measures is __________ 
3.Two angles forming a linear pair are $\qquad$
4. If two adjacent angles are supplementary, they form a ___________
5. If two lines intersect a point, then the vertically opposite angles are always ____________
6. 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 ______
Answer:

(i) $90^{\circ}$ (ii) $180^{\circ}$ (iii) supplementary
(iv) linear pair
(v) equal
(vi) obtuse angles

Ex 5.1 Question 10.

In the adjoining figure, name the following pairs of angles:

1. Obtuse vertically opposite angles.
2. Adjacent complementary angles.
3. Equal supplementary angles.
4. Unequal supplementary angles.
5. Adjacent angles that do not form a linear pair.

Answer:

(i) Obtuse vertically opposite angles means greater than $90^{\circ}$ and equal $\angle \mathrm{AOD}=$ $\angle \mathrm{BOC}$.
(ii) Adjacent complementary angles means angles have common vertex, common arm, noncommon arms are on either side of common arm and sum of angles is $90^{\circ}$.
(iii) Equal supplementary angles means sum of angles is $180^{\circ}$ and supplement angles are equal.
(iv) Unequal supplementary angles means sum of angles is $180^{\circ}$ and supplement angles are unequal.
i.e., $\angle \mathrm{AOE}, \angle \mathrm{EOC} ; \angle \mathrm{AOD}, \angle \mathrm{DOC}$ and $\angle \mathrm{AOB}, \angle \mathrm{BOC}$
(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., $\angle \mathrm{AOB}, \angle \mathrm{AOE} ; \angle \mathrm{AOE}, \angle \mathrm{EOD}$ and $\angle \mathrm{EOD}, \angle \mathrm{COD}$