RS Aggarwal Solutions Class 7 Maths Chapter 13 Ex 13.1 (Updated For 2024)

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RS Aggarwal Solutions Class 7 Maths Chapter 13 Ex 13.1

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Question 1.
Solution:
(i) The given angle = 35°
Let x be its complementary, then
x + 35° = 90°
⇒ x = 90° – 35° = 55°
Complement angle = 55°
(ii) The given angle = 47°
Let x be its complement, then
x + 47° = 90 ⇒ x = 90° – 47° = 43°
Complement angle = 43°
(iii) The given angles = 60°
Let x be its complement angle
x + 60° = 90° ⇒ x = 90° – 60° = 30°
Complement angle = 30°
(iv) The given angle = 73°
Let x be its complement angle
x + 73° = 90°
⇒ x = 90° – 73° = 17°
Complement angle = 17°

Question 2.
Solution:
(i) Given angle = 80°
Let x be its supplement angle, then
x + 80° = 180°
⇒ x = 180° – 80° = 100°
Supplement angle = 100°
(ii) Given angle = 54°
Let x be its supplement angle, then
x + 54° = 180°
⇒ x = 180° – 54° = 126°
Supplement angle = 126°
(iii) Given angle = 105°
let x be its supplement angle, then
x + 105° = 180°
⇒ x = 180° – 105° = 75°
Supplement angle = 75°
(iv) Given angle = 123°
Let x be its supplement angle, then
x + 123° = 180°
⇒ x = 180° – 123° = 57°
⇒ Supplement angle = 57°

Question 3.
Solution:
Let smaller angle =x
Then larger angle = x + 36°
But x + x + 36° = 180° (Angles are supplementary)
2x = 180° – 36°= 144°
x = 72°
Smaller angle = 72°
and larger angle = 72° + 36° = 108°

Question 4.
Solution:
Let angle be = x
Then other supplement angle = 180°- x
x = 180° – x
⇒ x + x = 180°
⇒ 2x = 180°
⇒ x = 90°
Hence angles are 90°, and 90°

Question 5.
Solution:
Sum of two supplementary angles is 180°
If one is acute, then second will be obtuse or both angles will be equal
Hence both angles can not be acute or obtuse
Both can be right angles only

Question 6.
Solution:
In the given figure,
AOB is a straight line and the ray OC stands on it.
∠AOC = 64° and ∠BOC = x°

∠AOC + ∠BOC = 180° (Linear pair)
⇒ 64° + x = 180°
⇒ x = 180° – 64° = 116°
Hence x = 116°

Question 7.
Solution:
AOB is a straight line and ray OC stands on it ∠AOC = (2x – 10)°, ∠BOC = (3x + 20)°

∠AOC + ∠BOC = 180° (Linear pair)
⇒ 2x – 10° + 3x + 20° = 180°
⇒ 5x + 10° = 180°
⇒ 5x = 170°
⇒ x = 34°
∠AOC = (2x – 10)° = 2 x 34° – 10 = 68° – 10° = 58°
∠BOC = (3x + 20)° = 3 x 34° + 20° – 102° + 20° = 122°

Question 8.
Solution:
AOB is a straight line and rays OC and OD stands on it ∠AOC = 65°, ∠BOD = 70° and ∠COD = x

But ∠AOC + ∠COD + ∠BOD = 180° (Angles on one side of the straight line)
⇒ 65° + x + 70° = 180°
⇒ 135° + x = 180°
⇒ x = 180° – 135°
⇒ x = 45°
Hence x = 45°

Question 9.
Solution:
Two straight lines AB and CD intersect each other at O.

∠AOC = 42°
AB and CD intersect each other at O.
∠AOC = ∠BOD (Vertically opposite angles)
and ∠AOD = ∠BOC
But ∠AOC = 42°
∠BOD = 42°
AOB is a straight line and OC stands on it
∠AOC + ∠BOC = 180°
⇒ 42° = ∠BOC = 180°
⇒ ∠BOC = 180° – 42° = 138°
But ∠AOD = ∠BOC (vertically opposite angles)
∠AOD = 138°
Hence ∠AOD = 138°, ∠BOD = 42° and ∠COB =138°

Question 10.
Solution:
Two straight lines PQ and RS intersect at O.
∠POS = 114°
Straight lines

PQ and RS intersect each other at O
∠POS = ∠QOR (Vertically opposite angles)
But ∠POS = 114°
∠QOR = 114° or ∠ROQ = 114°
But ∠POS + ∠POR = 180° (Linear pair)
⇒ 114° + ∠POR = 180°
⇒ ∠POR = 180° – 114° = 66°
But ∠QOS = ∠POR (vertically opposite angles)
∠QOS = 66°
Hence ∠POR = 66°, ∠ROQ =114° and ∠QOS = 66°

Question 11.
Solution:
In the given figure, rays OA, OB, OC and OD meet at O and ZAOB – 56°,
∠BOC = 100°, ∠COD = x and ∠DOA = 74°

But ∠AOB + ∠BOC + ∠COD + ∠DOA = 360° (Angles at a point)
56° + 100° + x° + 74° = 360°
⇒ 230° + x° = 360°
⇒ x° = 360° – 230° = 130°
⇒ x = 130°

RS Aggarwal Solutions Class 7 Maths Chapter 13 Ex 13.1 – Overview

Basic Concepts 

Here are the basic concepts of this exercise:

• Adjacent and Vertical Angles
• Complementary Angles
• Supplementary Angles
• Alternate Angles

Important Topics

Here are the important topics you must cover

• Introduction
• Related Angles
• Complementary angles
• Supplementary angles
• Adjacent angles
• Linear pair
• Vertically opposite angles
• Pairs of Lines
• Intersecting lines
• Transversal
• Angles made by the transversal
• Transversal of Parallel Lines
• Checking for Parallel Lines

Definitions

1. Line: A figure that can be extended as much as you want in opposite directions without any obligations to having the endpoints is called a line. 
2. Ray: The completely straight line that starts from a fixed point moving only in one direction is called a ray.
3. Line Segment: It can be defined as the line made using the two definite starting and ending points. It doesn’t have any thickness & is only a one-dimensional figure.
4. Angle: An angle is formed when the two line segments are joined at a single point. It is a combination of at least two line segments meeting at a common point, called as the vertex of the angle. The sides/arms of the formed angle are those two line segments only.

Types OF Angles

There are 6 types of angles, mentioned below:

1. Acute Angle: It can be defined as angles less than 90 degrees.
2. Obtuse Angle: An angle that can be defined as an angle more than 90 degrees.
3. Right Angle: An angle that can be defined as an angle formed exactly at 90 degrees.
4. Straight Angle: An angle that can be defined as an angle formed exactly at 180 degrees.
5. Reflex Angle: Angle: An angle that can be defined as an angle of mof or 180 degrees but less than 270 degrees.
6. Full Angle: An angle that can be defined as an angle formed exactly at 360 degrees.

Related Angles

Apart from the other six angles, here are some related angles you should know about.

1. Complementary Angle: When the sum of two angles measures is equivalent to 90°, then we call it the Complementary Angle.
2. Supplementary Angle: When the sum of two angles measures is equivalent to 180°, then we call it the Supplementary Angle.
3. Adjacent Angle: These angles are the ones having a common vertex plus a common arm. Additionally, they do not possess any common interior points.
4. Linear pair: It can be defined as a pair of adjacent angles, and its non-common sides are the opposite rays.
5. Vertically Opposite Angles: The vertically opposite angles formed whenever the two lines intersect with each other are always equal.

Pairs Of Lines

1. Intersecting lines: The Intersection between two or more lines happens only if they have a common point. The common point symbolized as O is what we call their point of intersection.
2. Transversal: It can be defined as the Intersection between two or more lines at different points.
3. Angles made by the transversal: When the transversal cuts the lines, then multiple different angles are formed. They are:

• Interior angles
• Exterior angles
• Pairs of Alternate interior angles
• Pairs of Alternate exterior angles
• Pairs of Corresponding angles
• Pairs of interior angles (-Similar side of the transversal-)

4. Transversal of Parallel Lines: These lines do not meet anywhere. Also, the  Transversal of Parallel Lines gives birth to some interesting results.

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