CBSE Class 7 Mathematics Lines And Angles Worksheet Set 02

Question 1. In the fig four line segments PQ ,QR,RS and ST are making the letter W ,PQ || RS and QR || ST . If angle between PQ and QR is 39°, find the value of x and y

Answer:
We are given that \( PQ \parallel RS \) and \( QR \) acts as a transversal line.
Since alternate interior angles are equal:
\( x = \angle PQR = 39^\circ \)
Similarly, we have \( QR \parallel ST \) and \( RS \) acts as a transversal line.
Therefore, the alternate interior angles are equal:
\( y = x = 39^\circ \)
So, both \( x \) and \( y \) are equal to \( 39^\circ \).
In simple words: Because the lines are parallel, the angles inside that look like a Z-shape are equal. This means both x and y are equal to 39 degrees.

Exam Tip: Remember that alternate interior angles form a 'Z' or 'S' shape when lines are parallel. Identifying this shape helps you solve angle puzzles quickly.

Question 2. Out of a pair of complementary angles, one is \(\frac{2}{3}\) of the other. find the angles.
Answer:
Let one of the complementary angles be \( x \).
According to the given condition, the other angle is \( \frac{2}{3}x \).
Since they are complementary, their sum is \( 90^\circ \):
\( x + \frac{2}{3}x = 90^\circ \)
\( \implies \frac{5}{3}x = 90^\circ \)
\( \implies x = \frac{90^\circ \times 3}{5} \)
\( \implies x = 54^\circ \)
The other angle is:
\( \frac{2}{3} \times 54^\circ = 36^\circ \)
Therefore, the two angles are \( 36^\circ \) and \( 54^\circ \).
In simple words: Complementary angles always add up to 90 degrees. By setting up a simple fraction, we find that the two angles are 36 degrees and 54 degrees.

Exam Tip: Always double-check your final angles by adding them together. For complementary angles, the sum must always equal 90 degrees.

Question 3. In the fig CD intersects the line AB at F, \(\angle CFB = 50^\circ\) and \(\angle EFA = \angle AFD\). Find the measure of \(\angle EFC\).

Answer:
Given that line \( CD \) intersects line \( AB \) at point \( F \).
Since vertically opposite angles are equal:
\( \angle AFD = \angle CFB = 50^\circ \)
We are given that \( \angle EFA = \angle AFD \).
So, \( \angle EFA = 50^\circ \).
Now, points \( A \), \( F \), and \( B \) lie on a straight line \( AB \). The sum of angles on a straight line is \( 180^\circ \):
\( \angle CFB + \angle EFA + \angle EFC = 180^\circ \)
\( \implies 50^\circ + 50^\circ + \angle EFC = 180^\circ \)
\( \implies 100^\circ + \angle EFC = 180^\circ \)
\( \implies \angle EFC = 180^\circ - 100^\circ = 80^\circ \)
Therefore, the measure of \( \angle EFC \) is \( 80^\circ \).
In simple words: Since lines cross, the opposite angles are equal, making angle AFD 50 degrees. Adding the angles on the straight line together to reach 180 degrees shows us that angle EFC is 80 degrees.

Exam Tip: Vertically opposite angles are equal only when two straight lines intersect. Look for straight lines to locate these pairs easily.

Question 4. Measures of two supplementary angles are consecutive odd integers. Find the angles
Answer:
Let one of the supplementary angles be \( x \).
Since they are consecutive odd integers, the other angle is \( x + 2 \).
Since supplementary angles add up to \( 180^\circ \):
\( x + (x + 2) = 180^\circ \)
\( \implies 2x + 2 = 180^\circ \)
\( \implies 2x = 178^\circ \)
\( \implies x = 89^\circ \)
The other angle is:
\( x + 2 = 89^\circ + 2 = 91^\circ \)
Therefore, the two angles are \( 89^\circ \) and \( 91^\circ \).
In simple words: Supplementary angles always add up to 180 degrees. Two odd numbers next to each other that add up to 180 are 89 and 91.

Exam Tip: For consecutive odd numbers, always use \( x \) and \( x+2 \). Since their difference is always 2, this setup works for both odd and even consecutive numbers.

Question 5. In the fig PQ,RS and UT are parallel lines.
(i) if \( c=57^\circ \) and \( a = \frac{c}{3} \), find the value of \( d \)
(ii) \( c=75^\circ \) and \( a = \frac{2}{5}c \), find \( b \)
Answer:
(i) Given that \( c = 57^\circ \) and \( a = \frac{c}{3} \).
First, find the value of \( a \):
\( a = \frac{57^\circ}{3} = 19^\circ \)
Since PQ \(\parallel\) UT with the transversal line, we have:
\( a + b = c \)
\( \implies 19^\circ + b = 57^\circ \)
\( \implies b = 57^\circ - 19^\circ = 38^\circ \)
Since PQ \(\parallel\) RS with the transversal line, co-interior angles are supplementary:
\( b + d = 180^\circ \)
\( \implies 38^\circ + d = 180^\circ \)
\( \implies d = 180^\circ - 38^\circ = 142^\circ \)
So, the value of \( d \) is \( 142^\circ \).

(ii) Given that \( c = 75^\circ \) and \( a = \frac{2}{5}c \).
First, find the value of \( a \):
\( a = \frac{2}{5} \times 75^\circ = 30^\circ \)
Since PQ \(\parallel\) UT, we have:
\( a + b = c \).
\( \implies 30^\circ + b = 75^\circ \)
\( \implies b = 75^\circ - 30^\circ = 45^\circ \)
So, the value of \( b \) is \( 45^\circ \).
In simple words: When lines are parallel, we can use simple rules like alternate interior angles and co-interior angles adding up to 180 degrees to find the missing values.

Exam Tip: When dealing with multiple parallel lines, you can use any line as a transversal to connect angles on different levels.

Question 6. If a transversal intersects two parallel lines, and the difference of two interior angles on one side of the transversal is 20°, find the angles.
Answer:
Let the two interior angles on the same side of the transversal be \( x \) and \( y \).
Since interior angles on the same side of a transversal are supplementary, their sum is \( 180^\circ \):
\( x + y = 180^\circ \) ---(Equation 1)
We are given that the difference between these two angles is \( 20^\circ \):
\( x - y = 20^\circ \) ---(Equation 2)
Adding Equation 1 and Equation 2:
\( 2x = 200^\circ \)
\( \implies x = 100^\circ \)
Substituting the value of \( x \) into Equation 1:
\( 100^\circ + y = 180^\circ \)
\( \implies y = 80^\circ \)
Therefore, the two angles are \( 100^\circ \) and \( 80^\circ \).
In simple words: Interior angles on the same side of a transversal always add up to 180 degrees. If their difference is 20 degrees, the two angles must be 80 degrees and 100 degrees.

Exam Tip: Read carefully to identify if angles are supplementary or complementary before setting up your equations.

Question 7. Find the value of \(\angle BOC\), If points A, O and B are collinear

Answer:
Since points A, O, and B are collinear, the sum of all angles on the straight line AB at point O is \( 180^\circ \):
\( \angle AOD + \angle DOC + \angle BOC = 180^\circ \)
\( \implies (x - 10)^\circ + (4x - 25)^\circ + (x + 5)^\circ = 180^\circ \)
\( \implies x + 4x + x - 10 - 25 + 5 = 180 \)
\( \implies 6x - 30 = 180 \)
\( \implies 6x = 210 \)
\( \implies x = 35 \)
Now, we can find the measure of \( \angle BOC \):
\( \angle BOC = (x + 5)^\circ = (35 + 5)^\circ = 40^\circ \)
Therefore, the value of \( \angle BOC \) is \( 40^\circ \).
In simple words: Since A, O, and B lie on a straight line, all three angles add up to 180 degrees. Solving for x gives 35, which makes the angle BOC equal to 40 degrees.

Exam Tip: Remember that a straight line always has a total angle of 180 degrees. Setting the sum of all linear parts to 180 will give you the correct value of x.

Question 8. In the fig state which pair of lines are parallel. give reason

Answer:
From the given figure, we can observe the following:
At the intersection of line \( m \) and transversal \( l \), the angle vertically opposite to the interior angle is \( 120^\circ \).
Since vertically opposite angles are equal, the interior angle (let's call it \( \angle 1 \)) is also \( 120^\circ \).
Now, considering the lines \( m \) and \( n \) with the transversal \( l \):
The two interior angles on the same side of the transversal are \( \angle 1 = 120^\circ \) and \( 60^\circ \).
Let's find their sum:
\( 120^\circ + 60^\circ = 180^\circ \)
Since the sum of co-interior angles is \( 180^\circ \) (they are supplementary), the lines \( m \) and \( n \) are parallel to each other (\( m \parallel n \)).
In simple words: The two inside angles on the same side of the line crossing them add up to 180 degrees. Since they add up to exactly 180 degrees, the lines m and n must be parallel.

Exam Tip: To prove lines are parallel, show that either corresponding angles are equal, alternate interior angles are equal, or co-interior angles add up to 180 degrees.

Question 9. In the fig l, m and n are parallel lines, and the lines p and q are also parallel, find the value of a, b and c

Answer:
Given that lines \( l \parallel m \parallel n \) and transversals \( p \parallel q \).

1. Considering parallel lines \( l \) and \( m \) cut by transversal \( q \):
The corresponding angles are equal:
\( 6a = 120^\circ \)
\( \implies a = \frac{120^\circ}{6} = 20^\circ \)

2. Considering parallel transversals \( p \parallel q \) cut by line \( n \):
The corresponding angles are equal:
\( 4c = 120^\circ \)
\( \implies c = \frac{120^\circ}{4} = 30^\circ \)

3. Considering parallel lines \( m \) and \( n \) cut by transversal \( p \):
The corresponding angles are equal:
\( 3b = 4c \)
\( \implies 3b = 4 \times 30^\circ \)
\( \implies 3b = 120^\circ \)
\( \implies b = \frac{120^\circ}{3} = 40^\circ \)

Therefore, the values are \( a = 20^\circ \), \( b = 40^\circ \), and \( c = 30^\circ \).
In simple words: Since all these lines are parallel to each other, their corresponding angles are equal. We can easily find a, b, and c by matching the equal angles.

Exam Tip: Work step-by-step from one parallel intersection to another. Connecting different transversals using equal angles is a reliable strategy.

Question 10. In fig AB || CD. Find the reflex \(\angle EFG\)

Answer:
To find the reflex \( \angle EFG \), let us draw a line \( l \) through point \( F \) such that \( l \parallel AB \parallel CD \).
This parallel line divides \( \angle EFG \) into two parts, let's say \( \angle 1 \) and \( \angle 2 \).

1. Since \( l \parallel AB \) and \( EF \) is the transversal:
The alternate interior angles are equal:
\( \angle 1 = \angle AEF = 34^\circ \)

2. Since \( l \parallel CD \) and \( FG \) is the transversal:
The co-interior angles on the same side of the transversal are supplementary:
\( \angle 2 + \angle FGD = 180^\circ \)
\( \implies \angle 2 + 135^\circ = 180^\circ \)
\( \implies \angle 2 = 180^\circ - 135^\circ = 45^\circ \)

Now, we can find the total measure of \( \angle EFG \):
\( \angle EFG = \angle 1 + \angle 2 = 34^\circ + 45^\circ = 79^\circ \)

To find the reflex angle:
Reflex \( \angle EFG = 360^\circ - \angle EFG = 360^\circ - 79^\circ = 281^\circ \)

Therefore, the reflex \( \angle EFG \) is \( 281^\circ \).
In simple words: By drawing a middle parallel line, we break the angle into two smaller parts (34 degrees and 45 degrees) which add up to 79 degrees. Subtracting this from 360 degrees gives us the reflex angle of 281 degrees.

Exam Tip: Drawing an auxiliary parallel line is a very useful trick when you need to bridge angles between two parallel lines.

Subject: Science

Chapter-11: Respiration in plants and animals

Question 1. MATCH THE FOLLOWING:
a) Larynx - Fermentation
b) Guard Cell - Voice Box
c) Phenolphthalein - Stomata
d) Alcohol - Pink in Alkaline
Answer:
The correct matching pairs are as follows:
a) Larynx - Voice Box
b) Guard Cell - Stomata
c) Phenolphthalein - Pink in Alkaline
d) Alcohol - Fermentation
In simple words: The larynx is our voice box, guard cells control the stomata on leaves, phenolphthalein turns pink in bases, and alcohol is made during fermentation.

Exam Tip: Match-the-following questions are high-scoring. Carefully link known terms first, then deduce the remaining pairs.

Question 2. DEFINE THE FOLLOWING:
a) Respiration Rate
b) Fermentation
c) Aerobic Respiration
d) Diaphragm
Answer:
a) Respiration Rate: The number of times a living being breathes in a single minute is called its respiration rate.
b) Fermentation: This is a process in which glucose is broken down to release energy without the use of oxygen, typically by yeast, producing alcohol and carbon dioxide.
c) Aerobic Respiration: This is the type of respiration where food (glucose) is broken down in the presence of oxygen to release energy, carbon dioxide, and water.
d) Diaphragm: This is a wide, dome-shaped muscular sheet that forms the floor of the chest cavity and helps in breathing by moving up and down.
In simple words: Respiration rate is your breathing speed. Fermentation makes alcohol without oxygen. Aerobic respiration is breathing that uses oxygen. The diaphragm is the muscle that moves when you breathe.

Exam Tip: When defining biological terms, try to use simple but specific keywords like 'presence of oxygen' for aerobic respiration and 'muscular sheet' for diaphragm to get full marks.

Question 3. DRAW THE LABELLED DIAGRAMS
a) Lungs (Respiratory System)
a) Stomata
b) Alveoli
c) Guard Cell
Answer:
To draw these diagrams, focus on the following key parts to label:
a) Lungs (Respiratory System): Draw the trachea (windpipe) dividing into two bronchi, leading into the two lungs. Label the bronchioles and the rib cage.
a) Stomata: Draw the tiny openings found on the leaf surface. Label the stomatal pore and the guard cells surrounding it.
b) Alveoli: Draw the tiny, grape-like air sacs at the end of the bronchioles inside the lungs. Label the thin wall of alveoli and the surrounding blood capillaries.
c) Guard Cell: Draw two kidney-shaped cells that control the opening and closing of a stomata. Label the inner thick wall, outer thin wall, chloroplasts, and nucleus.
In simple words: When drawing, make sure to point out and label the main parts clearly so anyone can understand what the diagram shows.

Exam Tip: Always use a sharp pencil to draw diagrams, keep labels on one side if possible, and underline the title of your diagram.

Question 4. Answer the following
a) Describe the path taken by inhaled air from the nostrils to the lungs.
b) Why the respiratory rate increases after exercise?
c) How do fish and tadpole breath? How does an insect take in air and how does the air reach different part of the body?
d) Why do gardener loosen the soil from time to time?
Answer:
a) Path of inhaled air: The air we breathe in enters through our nostrils into the nasal cavity. It then passes down through the windpipe (trachea) and branches into two bronchi, which carry the air directly into our lungs.
b) Increase in respiratory rate after exercise: During exercise, our body needs more energy. To produce this energy, our cells need more oxygen to break down food. To meet this high demand, we breathe much faster and deeper to supply extra oxygen to our blood.
c) Breathing in fish, tadpoles, and insects:
- Fish and tadpoles breathe using special respiratory organs called gills, which absorb oxygen dissolved in water.
- Insects take in air through small pores on the sides of their bodies called spiracles. This air then travels through a network of air tubes (tracheae) that deliver oxygen directly to all body parts.
d) Why gardeners loosen soil: Loosening the soil creates small air spaces between the soil particles. This allows the plant roots to get the oxygen they need to breathe and grow, as root cells also require oxygen to survive.
In simple words: Air goes through your nose down to your lungs. Exercise makes us breathe fast because our muscles need more energy. Fish use gills, and insects use side-holes and tubes to breathe. Gardeners loosen soil so plant roots can get air.

Exam Tip: In answers with multiple sub-parts, write in clear bullet points or numbered sections to make it easy for the examiner to read and award full marks.