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All questions of Lines and Angles for Class 7 Exam

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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Lines and Angles, Class 7, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic. 
Q.
If two lines intersect at a point, then the vertically opposite angles are always ________
  • a)
    supplementary
  • b)
    equal
  • c)
    unequal
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Ananya Choudhary answered


Given two lines AB and CD intersect each other at the point O.
To prove: ∠1 = ∠3 and ∠2 = ∠4
Proof:
From the figure, ∠1 + ∠2 = 180 deg [Linear pair]  → (1)
∠2 + ∠3 = 180 deg [Linear pair]  → (2)
From (1) and (2), we get
∠1 + ∠2 = ∠2 + ∠3
∴ ∠1 = ∠3
Similarly, we can prove ∠2 = ∠4 also.

If two angles are supplementary then the sum of their measures is ___________ .
  • a)
    45°
  • b)
    180°
  • c)
    90°
  • d)
    360°
Correct answer is option 'B'. Can you explain this answer?

Shilpa Das answered
Supplementary angles are two angles whose sum is equal to 180∘. In other words when you add the measure of one angle in the pair with the other angle in the pair, they equal 180 degrees.

These two angles are supplementary because together they form a straight line. You can also tell that they are supplementary because when you add their angle measures the sum is equal to 180 degrees.

120+60=180degree

  • a)
    90°
  • b)
    30°
  • c)
    60°
  • d)
    180°
Correct answer is option 'C'. Can you explain this answer?

Ishu answered
Sum of two co-interior angle =180 then, 2x+x=180 3x=180 x=180/3=60

If two adjacent angles are supplementary, then they form _________ .
  • a)
    a linear pair of angles
  • b)
    vertically opposite angles
  • c)
    Corresponding angles
  • d)
    a ray
Correct answer is 'A'. Can you explain this answer?

Shilpa Das answered
A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary.

  • a)
    60°
  • b)
    90°
  • c)
    120°
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Varun Kapoor answered
120 and x are corresponding angles and corresponding angles are equal so x = 120°

  • a)
    120°
  • b)
    180°
  • c)
    60°
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Anveshi Shahi answered
In the above given figure we can clearly see that there are two lines named as l and m they both are parallel to each other. We can also write it like l||m. There is also a line which is cutting the lines l||m it is a transversal line it isn't named there. Let's suppose the name of transversal line is y. We can clearly see on the line y there is an angle named x and there is another angle of 60 degree. According to the maths rule of co-interior angle the sum of x and 60 degree must be 180 degree. So, x + 60= 180 x = 180-60 x = 120 Answer

Find the measure of an angle, if 7 times its complement is 10 less than 3 times its supplement
  • a)
    15°    
  • b)
    10°
  • c)
    25°
  • d)
    5°
Correct answer is option 'C'. Can you explain this answer?

Ananya Das answered
Let the angle be x
measure of its complement = (90-x)
measure of its supplement= (180-x)
7(90-x) =3(180-x)-10
630 - 7x=540x-3x -10
-7x+3x= 530-630
-4x=-100
x= 100/4
x=25

Find the angle, which is equal to its supplement.
  • a)
    60°
  • b)
    90°
  • c)
    120°
  • d)
    30°
Correct answer is option 'B'. Can you explain this answer?

Ananya Das answered
Supplementary angles sums up to 180° since 90° + 90° = 180°, 90° is supplementary to itself

Find the angle whose measure is five times its complement
  • a)
    360°
  • b)
    75°
  • c)
    180°
  • d)
    30°
Correct answer is option 'B'. Can you explain this answer?

Niti menon answered
This will be the equation x=5(90-x)
solution= x=5(90-x)              
                x+5x=450
                6x=450
                 6x/6=450/6   {divide by 6 to both the side to x}
                  x=75

ans= The angle is 15 degree and its compliment angle is 75 degree

In a right angled triangle where angle A= 90° and AB=AC. What are the values of angle B.      
  • a)
    45°      
  • b)
    35°      
  • c)
    75°      
  • d)
    65°
Correct answer is option 'A'. Can you explain this answer?

Anirudh Sengupta answered
∵ In ∆ABC,
AB = AC
∴ ∠B = ∠C    ...(1)
| Angles opposite to equal sides of a triangle are equal
In ∆ABC,
∠A + ∠B + ∠C = 180°
| Sum of all the angles of a triangle is 180°
⇒ 90° + ∠B + ∠C = 180°
| ∵ ∠A = 90° (given)
⇒    ∠B + ∠C = 90°    ...(2)
From (1) and (2), we get
∠B = ∠C = 45°.

In figure pair of alternate interior angles are :
  • a)
    ∠2, ∠5
  • b)
    ∠1, ∠2
  • c)
    ∠2, ∠3
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Geetika Shah answered
Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.
So in the given figure ∠2, ∠3 are alternate interior angles
Alternate angle form Z shape

What is the measure of the supplement of 54°?
  • a)
    126°
  • b)
    49°
  • c)
    35°
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Kiran Reddy answered
As we know for becoming supplementary angles, the sum of both the angles should be 180∘
Let the supplementary angle be x.
So, 54∘+x = 180∘
⇒ x = 126∘

Two angles forming a linear pair are ________________.
  • a)
    complimentary
  • b)
    equal
  • c)
    supplementary
  • d)
    None of these
Correct answer is 'C'. Can you explain this answer?

Meera Reddy answered
Supplementary angles are two angles whose sum is 180 degree. A linear pair (two angles that form a line) will always be supplementary. The two angles can be adjacent or non-adjacent.

A line that intersects two or more lines at distinct points is called
  • a)
    parallel
  • b)
    transversal
  • c)
    intersecting
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Meera Reddy answered
Parallel Lines and a Transversal. A line which intersects two or more given lines at distinct points is called a 'transversal' of the given lines.

Identify which of the following pairs of angles are complementary.
  • a)
    65°, 115°
  • b)
    130°, 50°
  • c)
    63°, 27°
  • d)
    112°, 68°
Correct answer is option 'C'. Can you explain this answer?

Seema desai answered
**Complementary Angles:**

Complementary angles are a pair of angles whose measures add up to 90 degrees. In other words, when you add the measures of two complementary angles, the sum will equal 90 degrees.

**Explanation:**

Let's analyze each pair of angles given and determine if they are complementary or not.

a) 65°, 115°: The sum of these angles is 65° + 115° = 180°, which is greater than 90°. Therefore, these angles are not complementary.

b) 130°, 50°: The sum of these angles is 130° + 50° = 180°, which is greater than 90°. Therefore, these angles are not complementary.

c) 63°, 27°: The sum of these angles is 63° + 27° = 90°. This sum is exactly 90°, which means these angles are complementary.

d) 112°, 68°: The sum of these angles is 112° + 68° = 180°, which is greater than 90°. Therefore, these angles are not complementary.

Therefore, the pair of angles that is complementary is **c) 63°, 27°**.

What is the measure of the complement of 65°?
  • a)
    25°
  • b)
    55°
  • c)
    65°
  • d)
    45°
Correct answer is option 'A'. Can you explain this answer?

Prisha Mehta answered
Let's find the complement of 65°
Complement of an angle is the angle that when added to it gives 90°.
So, if x is the complement of 65°, then:
  • x + 65° = 90°
To find x, subtract 65° from both sides:
  • x = 90° - 65°
  • x = 25°
Therefore, the complement of 65° is 25°.

The sum of the measures of the angles in a linear pair is
  • a)
    90°
  • b)
    180°
  • c)
    360°
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Chirag Yadav answered
The Concept of Linear Pair
A linear pair of angles is formed when two lines intersect. The angles that are adjacent to each other and share a common side are referred to as a linear pair.
Sum of Angles in a Linear Pair
- The two angles in a linear pair always lie on a straight line.
- A straight line measures 180 degrees.
Conclusion
- Therefore, the sum of the measures of the angles in a linear pair is always 180 degrees.
- This is why the correct answer is option 'B'.
Important Points to Remember
- Linear pairs are always supplementary, which means their angles add up to 180 degrees.
- This property is fundamental in geometry and helps in solving various problems involving angles.
Understanding this concept is crucial for further studies in geometry and helps in visualizing how angles interact with each other.

The sum of all angles around a point is
  • a)
    0deg
  • b)
    180deg
  • c)
    360deg
  • d)
    90deg
Correct answer is option 'C'. Can you explain this answer?

Partho Basu answered
The sum of all angles around a point is 360 degrees.

Explanation:


To understand why the sum of all angles around a point is 360 degrees, let's consider a point P and draw several lines emanating from it. Each of these lines creates an angle with its adjacent line. We can number these angles as shown below:

```
__1__
| |
2| P |3
|_____|
__4__
| |
5| |6
|_____|
__7__
| |
8| |9
|_____|
```

Angles formed by the lines:


- Angle 1 is formed between line 1 and line 2.
- Angle 2 is formed between line 2 and line 3.
- Angle 3 is formed between line 3 and line 4.
- Angle 4 is formed between line 4 and line 5.
- Angle 5 is formed between line 5 and line 6.
- Angle 6 is formed between line 6 and line 7.
- Angle 7 is formed between line 7 and line 8.
- Angle 8 is formed between line 8 and line 9.
- Angle 9 is formed between line 9 and line 1.

Sum of all angles:


If we add up all these angles, we get:

Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 + Angle 6 + Angle 7 + Angle 8 + Angle 9

This can be rewritten as:

Angle 1 + (Angle 2 + Angle 3) + (Angle 4 + Angle 5) + (Angle 6 + Angle 7) + (Angle 8 + Angle 9)

Notice that the sum of the adjacent angles (Angle 2 + Angle 3, Angle 4 + Angle 5, etc.) gives us a straight line. And since a straight line forms a 180-degree angle, we can simplify the expression further:

Angle 1 + 180 degrees + 180 degrees + 180 degrees + 180 degrees

Simplifying the expression, we get:

Angle 1 + 4 * 180 degrees

Since angle 1 is formed by two adjacent lines, it is a straight angle and measures 180 degrees. Therefore:

180 degrees + 4 * 180 degrees = 180 degrees + 720 degrees = 900 degrees

Thus, the sum of all angles around a point is 900 degrees. However, we know that a full rotation around a point is 360 degrees. Therefore, we subtract one full rotation (360 degrees) from the sum to get the final answer:

900 degrees - 360 degrees = 540 degrees

So, the sum of all angles around a point is 540 degrees.

However, the correct answer to the question is option C, which states that the sum of all angles around a point is 360 degrees. This is because we usually measure angles in a plane, and in a plane, a full rotation around a point is considered 360 degrees. Therefore, the sum of all angles around a point is 360 degrees.

In the following figure, a transversal cuts two parallel lines l and m at points G and H respectively and the angles thus formed are marked. If ∠1 is an acute angle, then, which of the following statements is false?
  • a)
    ∠1 + ∠2 = 180°
  • b)
    ∠2 + ∠5 = 180°
  • c)
    ∠3 + ∠8 = 180°
  • d)
    ∠2 + ∠6 = 180°
Correct answer is option 'D'. Can you explain this answer?

Sumita Singh answered
Understanding Angles Formed by a Transversal
When a transversal intersects two parallel lines, several angles are formed. The relationships between these angles can help determine which statements are true or false.
Angle Relationships
1. Corresponding Angles: Angles in the same position relative to the parallel lines are equal.
2. Alternate Interior Angles: Angles on opposite sides of the transversal but inside the parallel lines are equal.
3. Consecutive Interior Angles: Angles on the same side of the transversal and inside the parallel lines are supplementary, meaning they add up to 180 degrees.
Analysis of the Given Options
- a) ∠1 + ∠2 = 180°
This statement is true because ∠1 and ∠2 are consecutive interior angles.
- b) ∠2 + ∠5 = 180°
This statement is true because ∠2 and ∠5 are also consecutive interior angles.
- c) ∠3 + ∠8 = 180°
This statement is true as ∠3 and ∠8 are alternate interior angles, which are equal.
- d) ∠2 + ∠6 = 180°
This statement is false. ∠2 and ∠6 are not supplementary; they are corresponding angles and are equal, not adding up to 180 degrees.
Conclusion
The false statement among the options is d) ∠2 + ∠6 = 180°. Understanding the relationships between angles formed by a transversal cutting through parallel lines is crucial for solving geometry problems.

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
  • a)
    45°      
  • b)
    35°      
  • c)
    75°      
  • d)
    65°
Correct answer is option 'A'. Can you explain this answer?

Pranjal Banerjee answered
Given,
∠A = 90° and AB = AC
A/q,
AB = AC 
⇒ ∠B = ∠C (Angles opposite to the equal sides are equal.)
Now,
∠A + ∠B + ∠C = 180° (Sum of the interior angles of the triangle.)
⇒ 90° + 2∠B = 180°
⇒ 2∠B = 90° 
⇒ ∠B = 45°
Thus, ∠B = ∠C = 45°

Chapter doubts & questions for Lines and Angles - Mathematics (Maths) Class 7 2025 is part of Class 7 exam preparation. The chapters have been prepared according to the Class 7 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 7 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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