Andhra Pradesh SCERT Class 7 Maths Lines and Angles Question and Answers Solutions
Andhra Pradesh SCERT 7th Class Maths Solutions Chapter 5 Lines and Angles Question and answers. Students who are searching for Andhra Pradesh Class 7 Maths Chapter 5 can find here Solution of this chapter.
Board |
Andhra Pradesh (AP Board) |
Class |
7th |
Subject |
Maths |
Topic |
Solution |
EXERCISE 5.1
1.) Find the complement of each of the following angles:
ANSWER:
Here we have to find complement of given angle.
Given angle is 200
We know,
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
200 + complement of given angle = 90°
Complement of given angle = 90° – 200
Complement of given angle = 70°
ANSWER:
Here we have to find complement of given angle.
Given angle is 630
We know,
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
630+ complement of given angle = 90°
Complement of given angle = 90° – 630
Complement of given angle = 27°
ANSWER:
Here we have to find complement of given angle.
Given angle is 570
We know,
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
570 + complement of given angle = 90°
Complement of given angle = 90° – 570
Complement of given angle = 33°
2.) Find the supplement of each of the following angles:
ANSWER:
Here we have to find supplement of given angle.
Given angle is 1050
We know,
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
1050 + supplement of given angle = 180°
Supplement of given angle = 180° – 1050
Supplement of given angle = 75°
ANSWER:
Here we have to find supplement of given angle.
Given angle is 870
We know,
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
870 + Supplement of given angle = 180°
Supplement of given angle = 180° – 870
Supplement of given angle = 93°
ANSWER:
Here we have to find supplement of given angle.
Given angle is 1540
We know,
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
1540 + Supplementof given angle = 180°
Supplement of given angle = 180° – 1540
Supplement of given angle = 26°
3.) Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 65º, 115º (ii) 63º, 27º (iii) 112º, 68º
(iv) 130º, 50º (v) 45º, 45º (vi) 80º, 10º
ANSWER:
Here we have to find from given pairs of angles which are complementary and which are supplementary.
We know,
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
Pair (ii) 63º, 27º has sum 90° the angles are called complementary angles.
Pair (v) 45º, 45º has sum 90° the angles are called complementary angles.
Pair (vi) 80º, 10º has sum 90° the angles are called complementary angles.
Now,
We know,
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
Pair (i) 65º, 115º has sum 180° the angles are called supplementary angles.
Pair (iii) 112º, 68º has sum 180° the angles are called supplementary angles.
Pair (iv) 130º, 50º has sum 180° the angles are called supplementary angles.
4.) Find the angle which is equal to its complement.
ANSWER:
We have to find the angle which is equal to its complement.
Let, x is the angle which is equal to its complement.
We know,
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
X + X = 90°
2X = 90°
X = 90°/2
X = 45°
The angle which is equal to its complement is 45°
5.) Find the angle which is equal to its supplement.
ANSWER:
We have to find the angle which is equal to its supplement.
Let, x is the angle which is equal to its supplement.
We know,
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
X + X = 180°
2X = 180°
X = 180°/2
X = 90°
The angle which is equal to its supplement is 90°
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.
ANSWER:
Given that,
∠1 and ∠2 are supplementary angles.
When ∠1 is decreased then ∠2 is increases and both the angles still remain supplementary.
7.) Can two angles be supplementary if both of them are:
(i) acute? (ii) obtuse? (iii) right?
ANSWER:
We know,
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
Two angles be supplementary if both of them are right angles.
Only right angles has sum 180°.
90°+ 90°= 180°.
8.) An angle is greater than 45º. Is its complementary angle greater than 45º or equal to 45º or less than 45º?
ANSWER:
Here, angle is greater than 45º
We have to find its complementary angle greater than 45º or equal to 45º or less than 45º.
We know,
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
Angle is greater than 45º + its complementary angle = 90°
Complementary angle = 90° – Angle is greater than 45º
Complementary angle = less than 45º
9.) Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is _______.
ANSWER:
If two angles are complementary, then the sum of their measures is 90°
(ii) If two angles are supplementary, then the sum of their measures is ______.
ANSWER:
If two angles are supplementary, then the sum of their measures is 180°
(iii) If two adjacent angles are supplementary, they form a ___________.
ANSWER:
If two adjacent angles are supplementary, they form a linear pair.
10.) In the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
ANSWER:
We have to find Obtuse vertically opposite angles
Obtuse vertically opposite angles are ∠AOD, ∠BOC
(ii) Adjacent complementary angles
ANSWER:
We have to find adjacent complementary angles
Adjacent complementary angles are ∠EOA, ∠AOB
(iii) Equal supplementary angles
ANSWER:
We have to find Equal supplementary angles
Equal supplementary angles are ∠EOB, ∠EOD
(iv) Unequal supplementary angles
ANSWER:
We have to find Unequal supplementary angles
Unequal supplementary angles are ∠EOA, ∠EOC
(v) Adjacent angles that do not form a linear pair
ANSWER:
We have to find Adjacent angles that do not form a linear pair
Adjacent angles that do not form a linear pair are
i) ∠AOB, ∠AOE
ii) ∠AOE, ∠EOD
iii) ∠EOD, ∠COD
EXERCISE 5.2
1.) State the property that is used in each of the following statements?
(i) If a || b, then ∠1 = ∠5.
ANSWER:
Here, a || b, then ∠1 = ∠5.
Here, Corresponding angle property is used.
(ii) If ∠4 = ∠6, then a || b.
ANSWER:
Here, ∠4 = ∠6, then a || b.
Here, Alternate interior angle property is used.
(iii) If ∠4 + ∠5 = 180°, then a || b.
ANSWER:
Here, ∠4 + ∠5 = 180°, then a || b.
Here, we use interior angles on the same side of the transversal are supplementary.
2.) In the adjoining figure, identify
(i) the pairs of corresponding angles.
ANSWER:
Here we have to find the pairs of corresponding angles.
The pairs of corresponding angles are
- i) ∠1, ∠5
- ii) ∠2, ∠6
iii) ∠3, ∠7
- iv) ∠4, ∠8
(ii) the pairs of alternate interior angles.
ANSWER:
Here we have to find the pairs of alternate interior angles.
The pairs of alternate interior angles are
i) ∠2, ∠8
ii) ∠3, ∠5
(iii) the pairs of interior angles on the same side of the transversal.
ANSWER:
Here we have to find the pairs of interior angles on the same side of the transversal
The pairs of interior angles on the same side of the transversal are
i) ∠2, ∠5
ii) ∠3, ∠8
(iv) the vertically opposite angles.
ANSWER:
Here we have to find the vertically opposite angles.
The vertically opposite angles are
- i) ∠1, ∠3
- ii) ∠2, ∠4
iii) ∠5, ∠7
- iv) ∠6, ∠8
3.) In the adjoining figure, p || q. Find the unknown angles.
ANSWER:
In given figure, we have to find unknown angles.
We know,
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
∠d = 1250
∠e = ∠a
∠f = ∠c
We know,
If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary.
∠e + 1250 = 1800
∠e = 550
But ∠e = ∠a = 550
Now,
∠f + ∠d = 1800
∠f + 1250 = 1800
∠f = 550
But, ∠f = ∠c
∠c = 550
Now,
∠a + ∠b = 1800
550 + ∠b = 1800
∠b = 1250
4.) Find the value of x in each of the following figures if l || m
ANSWER:
Here, l || m
We have to find value of x.
We know,
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
Adjacent angle of x = 1100
We know,
If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary.
Adjacent angle of x + x = 1800
1100 + x = 1800
x = 1800 – 1100
x = 700
ANSWER:
Here, l || m
We have to find value of x.
We know,
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
X = 1000 …………………… (Corresponding angles)
5.) In the given figure, the arms of two angles are parallel.
If ∠ABC = 70º, then find
(i) ∠DGC
ANSWER:
Given that, the arms of two angles are parallel.
We have to find ∠DGC.
We know,
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
∠ABC = ∠DGC …………………… (Corresponding angles)
But, ∠ABC =700
∠DGC =700
(ii) ∠DEF
ANSWER:
Given that, the arms of two angles are parallel.
We have to find ∠DEF
We know,
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
∠ABC =∠DEF …………………… (Corresponding angles)
But, ∠ABC =700
∠DEF =700
6.) In the given figures below, decide whether l is parallel to m.
ANSWER:
We have to decide whether l is parallel to m.
When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.
1260 + 440 = 1700
Which is not equal to 1800
l is not parallel to m.
ANSWER:
We have to decide whether l is parallel to m.
When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
750 = adjacent angle of 750
Now,
750 + adjacent angle of 750 = 1800
750 + 750 = 1500
Which is not equal to 1800
l is not parallel to m.
ANSWER:
We have to decide whether l is parallel to m.
When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
570 = adjacent angle of 1230 ————– (corresponding angles)
Now,
1230 + adjacent angle of 1230 = 1800
1230 + 570 = 1800
Which is equal to 1800
l is parallel to m.
ANSWER:
We have to decide whether l is parallel to m.
When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
980 = adjacent angle of 720 ————– (corresponding angles)
Now,
720 + adjacent angle of 720 = 1800
720 + 980 = 1700
Which is not equal to 1800
l is not parallel to m.