Exercise 4.2 - Chapter 4 Geometry Term 1 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex 4.2
Question 1 .
Use any number of the given dots to make different angles.

Solution:

Question 2.

Name the vertex and sides that form each angle.

Solution:

Question $3 .$
Pick out the Right angles from the given figures.

Solution:
(i), (iii) and (v) are Right Angles.

Question $4 .$
Pick out the Acute angles from the given figures.

Solution:

(i), (iii) and (iv) are the Acute Angles.

Question 5 .
Pick out the Obtuse Angles from the given figures.

Solution:
(i) and (ii) are the Obtuse Angles.

Question 6 .
Name the angle in each figure given below in all the possible ways.

Solution:
(i) $\angle \mathrm{M}$ or $\angle \mathrm{LMN}$ or $\angle \mathrm{NML}$
(ii) $\angle \mathrm{Q}$ or $\angle \mathrm{PQR}$ or $\angle \mathrm{RQP}$
(iii) $\angle \mathrm{N}$ or $\angle \mathrm{MNO}$ or $\angle \mathrm{ONM}$
(iv) $\angle \mathrm{A}$ or $\angle \mathrm{TAS}$ or $\angle \mathrm{SAT}$
(v) $\angle \mathrm{Y}$ or $\angle \mathrm{XYZ}$ or $\angle \mathrm{ZYX}$
(vi) There are 3 angles in (vi)
- $\angle \mathrm{ADC}$ or $\angle \mathrm{CDA}$
- $\angle \mathrm{CDB}$ or $\angle \mathrm{BDC}$
- $\angle \mathrm{D}$ or $\angle \mathrm{ADB}$ or $\angle \mathrm{BDA}$
 

Question $7 .$
Say True or False.
1. $20^{\circ}$ and $70^{\circ}$ are complementary.
2. $88^{\circ}$ and $12^{\circ}$ are complementary.
3. $80^{\circ}$ and $180^{\circ}$ are supplementary.
4. $0^{\circ}$ and $180^{\circ}$ are supplementary.
Solution:
1. True
2. False
3. False
4. True

Question 8 .
Draw and label each of the angles
(i) $\angle \mathrm{NAS}=90^{\circ}$
(ii) $\angle B L G=35^{\circ}$
(iii) $\angle \mathrm{SMC}=145^{\circ}$
Solution:

Question $9 .$
Identify the types of angles shown by the hands of the given clock.

Solution:
(i) Obtuse Angle.
(ii) Zero Angle.
(iii) Straight Angle.
(iv) Acute Angle.
(v) Right Angle.

Question 10 .
Find the supplementary 'l' complementary angles in each case.

Solution:
(i) If two angles add up to $180^{\circ}$, they are supplementary.
We know that the straight angle $\angle \mathrm{CBC}=180^{\circ}$
Given $\angle \mathrm{CBD}=25^{\circ}$
$\therefore \angle \mathrm{DBA}=180^{\circ}-25^{\circ}=155^{\circ}$
$\therefore$ Supplementary $\angle \mathrm{DBA}=155^{\circ}$
(ii) If two angles add upto $90^{\circ}$, they are complementary
Given $\angle \mathrm{ABC}=25^{\circ}$
$\angle \mathrm{CBD}=30^{\circ}$
$\therefore \angle \mathrm{DBA}=90^{\circ}-30^{\circ}=60^{\circ}$
$\therefore$ Complementary angle $\angle \mathrm{DBA}=60^{\circ}$
(iii) Given $\angle \mathrm{CBA}=90^{\circ}$
$\angle \mathrm{CBD}=46^{\circ}$
$\therefore \angle \mathrm{DBA}=90^{\circ}-46^{\circ}=44^{\circ}$
We know that the sum of two angles is $90^{\circ}$, then they are complementary
$\therefore$ Complementary angle $\angle \mathrm{DBA}=44^{\circ}$

(iv) Given $\angle \mathrm{DBE}=180^{\circ}$
$\angle \mathrm{DBC}=67^{\circ}$
$\therefore \angle \mathrm{CBE}=180^{\circ}-67^{\circ}=113^{\circ}$
Here $\angle \mathrm{DBC}+\angle \mathrm{DBE}=180^{\circ}$
$\therefore$ Supplementary angle $\angle \mathrm{CBE}=113^{\circ}$
 

Objective Type Questions
Question $11 .$
In this Figure, which is not the correct way of naming an angle?

(a) $\angle \mathrm{Y}$
(b) $\angle \mathrm{ZXY}$
(c) $\angle \mathrm{ZYX}$
(d) $\angle \mathrm{XYZ}$
Solution:
(b) $\angle \mathrm{ZXY}$
 

Question 12 .
In this Figure, $\angle \mathrm{AYZ}=45^{\circ}$. If the point ' $\mathrm{A}$ ' is shifted to point ' $\mathrm{B}$ ' along the ray, then the measure of $\angle B Y Z$ is

(a) more than $45^{\circ}$
(b) $45^{\circ}$
(c) less than $45^{\circ}$
(d) $90^{\circ}$

Solution:
(b) $45^{\circ}$
Hint: $\angle \mathrm{XYZ}=\angle \mathrm{BYZ}=\angle \mathrm{AYZ}$