Lines and Angles Class 7 Worksheet with Answers

Geometry is another important concept in mathematics. Chapter 12 of the CBSE Class 7 Maths syllabus deals with Lines and Angles, which helps Grade 7 students improve their understanding of lines, measuring angles, and naming different types of angles. It also helps them learn how to solve geometric problems easily.

Students can download this CBSE Class 7 Maths Worksheet for Chapter 12 Lines and Angles (PDF) and solve the questions on their own. After solving, they can also cross-check their answers.

The Lines and Angles Class 7 Worksheet with Answers, along with NCERT Solutions for Class 7 Maths Chapter 12 and Class 7 Maths MCQs, is more than enough to understand this chapter well.

What are Lines?

A line is a straight path that goes on forever in both directions.

It doesn’t have a starting point or an ending point.

We usually show a line with arrows on both ends.

Example:

If you stretch a thread tightly, it looks like a straight line.

In geometry, we write it as Line AB (↔) — this means the line passes through points A and B.

Also Check: Simple Equations Class 7 Worksheet | Data Handling Class 7 Worksheet

Types of Lines

• Line Segment: Has a starting and ending point (like a pencil).
• Ray: Ray Has one starting point and then goes on forever in one direction (like sunlight).
• Parallel Lines: Parallel Lines are lines that never meet, no matter how far they go (like railway tracks).
• Intersecting Lines: Lines that cross each other at a point (like scissors).

What are Angles?

An angle is formed when two rays meet at a point.
The meeting point is called the vertex of the angle.

Example:

• If you open a door slightly, the space between the door and the wall makes an angle!
• We measure angles in degrees (°) using a protractor.

Also Check: NCERT Solutions for Class 7 Maths | Comparing Quantities Class 7 Worksheet

Types of Angles

Example from Daily Life:

• The corner of a window makes a right angle.
• The hands of a clock at 3 o’clock form a right angle.
• The scissors blades form an acute or obtuse angle depending on how open they are.

Why Do Class 7 Students Need Lines and Angles Worksheet ?

• Lines and Angles worksheets make learning geometry more fun and clear.
• When you practice these questions, one can actually see how lines meet and angles form it’s like solving small puzzles that help you think deeply.
• These worksheets don’t just help to score better; but also help to understand how geometry works in real life like in buildings, art, and even road signs.
• By practising regularly, students feel more confident and prepared for higher classes because then you will more familiar with this topic.
• Each worksheet feel like discovering something new about shapes and space.

Also Check: BODMAS Questions Class 7 Worksheet

Lines and Angles Class 7 Worksheet – Set 1

Directions:

Answer the following questions carefully. Use a protractor or rough diagram if needed.

1. Define an acute angle in your own words and give one real-life example.
   Answer: An acute angle is less than 90°. Example: The hands of a clock at 2 o’clock.
2. What is the measure of a straight angle?
   Answer: 180°.
3. If two angles form a linear pair and one angle measures 65°, find the other angle.
   Answer: 180° – 65° = 115°.
4. Two complementary angles differ by 20°. Find both angles.
   Answer:
   Let smaller angle = x, then larger = x + 20°.
   x + (x + 20°) = 90°
   2x + 20° = 90°
   x = 35°, larger = 55°.
5. Identify the type of angle between the hands of a clock at 9 o’clock.
   Answer: Right angle (90°).
6. If ∠A = 3x + 10 and ∠B = 5x – 10 are supplementary, find ∠A and ∠B.
   Answer:
   (3x + 10) + (5x – 10) = 180°
   8x = 180°
   x = 22.5°
   ∠A = 77.5°, ∠B = 102.5°.
7. Name the pair of opposite rays in the figure below (students imagine a line AB with point O between A and B).
   Answer: Ray OA and Ray OB are opposite rays.
8. If two adjacent angles are supplementary, what type of pair do they form?
   Answer: Linear pair.
9. The measure of an angle is twice its complement. Find the angle.
   Answer:
   Let smaller = x, larger = 2x
   x + 2x = 90° → 3x = 90° → x = 30°, larger = 60°.
10. Draw and label one example each of:
    (a) Acute angle
    (b) Reflex angle
    (c) Right angle
    Answer:
    Students draw 45°, 270°, and 90° respectively.

Also Check: Factorisation Worksheet Class 7 | Integers Worksheet Class 7

Practice Worksheet on Lines and Angles for Class 7 (Set 2)

Directions:

Answer the following questions. Read each sentence carefully some may need reasoning, some may need calculation.

1. If one angle of a linear pair is 3 times the other, find both angles.
   Answer:
   Let smaller = x, larger = 3x
   x + 3x = 180° → 4x = 180° → x = 45°, larger = 135°.
2. The sum of two supplementary angles is always _______.
   Answer: 180°
3. Find the value of x if ∠A and ∠B are complementary and ∠A = 4x – 10°, ∠B = 2x + 10°.
   Answer:
   (4x – 10) + (2x + 10) = 90° → 6x = 90° → x = 15°.
4. In a triangle, one angle measures 70° and another 50°. Find the third angle.
   Answer: 180° – (70° + 50°) = 60°.
5. Two vertically opposite angles are represented as (3x – 5)° and (2x + 10)°. Find the value of x.
   Answer:
   3x – 5 = 2x + 10 → x = 15°.
6. Name the types of angles formed when:
   (a) Two lines intersect.
   (b) One line cuts another at 90°.
   Answer:
   (a) Vertically opposite angles
   (b) Right angles
7. If ∠A and ∠B are supplementary and ∠A = 2x + 30°, ∠B = 3x – 10°, find both angles.
   Answer:
   (2x + 30) + (3x – 10) = 180 → 5x + 20 = 180 → 5x = 160 → x = 32°
   ∠A = 94°, ∠B = 86°.
8. A line segment is divided into two equal parts by a point. What is that point called?
   Answer: Midpoint
9. True or False:
   (a) Complementary angles add up to 180°.
   (b) Reflex angle is greater than 180°.
   Answer:
   (a) False
   (b) True
10. If one angle is one-fourth of its supplement, find the angle.
    Answer:
    Let smaller = x, larger = 180 – x
    x = ¼(180 – x) → 4x = 180 – x → 5x = 180 → x = 36°, larger = 144°.

Lines and Angles Class 7 Worksheet Advanced Practice (With Answers)

Each question follows CBSE Class 7 guidelines.

1. Write the complementary angle of 38°.

Answer:
The sum of complementary angles = 90°
Let the other angle = x
So, 38° + x = 90°
x = 52°
Complementary angle = 52°

2. Write the supplementary angle of 125°.

Answer:
The sum of supplementary angles = 180°
Let the other angle = x
125° + x = 180°
x = 55°
Supplementary angle = 55°

3. Find the angle which is equal to its complement.

Answer:
Let the angle = x
Then, complement = 90° − x
Given, both are equal ⇒ x = 90° − x
2x = 90°
x = 45°
Angle = 45°

4. Find the angle which is equal to its supplement.

Answer:
Let the angle = x
Then, supplement = 180° − x
Given, both are equal ⇒ x = 180° − x
2x = 180°
x = 90°
Angle = 90°

5. Two complementary angles differ by 14°. Find both angles.

Answer:
Let smaller = x, then larger = x + 14°
x + (x + 14°) = 90°
2x + 14 = 90
x = 38°, larger = 52°
Angles = 38° and 52°

6. Find the value of x if two supplementary angles are (3x + 20)° and (2x + 10)°.

Answer:
(3x + 20) + (2x + 10) = 180°
5x + 30 = 180°
x = 30°
Angles = 110° and 70°

7. In a figure, ∠A and ∠B form a linear pair. If ∠A = 3x – 10° and ∠B = x + 50°, find both angles.

Answer:
(3x – 10) + (x + 50) = 180°
4x + 40 = 180°
x = 35°
∠A = 95°, ∠B = 85°
 Angles = 95° and 85°

8. Identify if the following are adjacent angles: ∠PQR and ∠SQR (where R is the common vertex).

Answer:
They share a common vertex (R) and a common arm (QR).
Yes, they are adjacent angles.

9. Two lines AB and CD intersect at O. If ∠AOC = 75°, find ∠BOD.

Answer:
Vertically opposite angles are equal.
∠AOC = ∠BOD = 75°
∠BOD = 75°

10. If ∠1 = 40° and ∠2 are vertically opposite, find ∠2.

Answer:
Vertically opposite angles are equal.
∠2 = ∠1 = 40°
∠2 = 40°

11. A line XY cuts two parallel lines AB and CD at points P and Q respectively. If ∠APQ = 110°, find ∠PQD.

Answer:
∠APQ and ∠PQD are alternate interior angles.
When lines are parallel, alternate angles are equal.
∠PQD = 110°

Also Check: Sets Class 7 Worksheet | Fractions and Decimals Class 7 Worksheet

12. Find the value of x if the angles (5x – 20)° and (3x + 4)° form a linear pair.

Answer:
(5x – 20) + (3x + 4) = 180°
8x – 16 = 180°
x = 24.5°
 Angles = 102.5° and 77.5°

13. In a figure, line PQ is parallel to RS, and a transversal intersects them. If one corresponding angle is 65°, find all corresponding angles.

Answer:
All corresponding angles are equal in measure.
All corresponding angles = 65°

14. Find the measure of each angle if two supplementary angles are equal.

Answer:
Let both angles = x
x + x = 180°
2x = 180°
x = 90°
Each angle = 90°

15. In a figure, lines AB and CD are parallel, and a transversal EF cuts them. If ∠1 = 70°, find:

(a) ∠2 (alternate angle)
(b) ∠3 (co-interior angle)

Answer:
(a) Alternate interior angles are equal ⇒ ∠2 = 70°
(b) Co-interior angles are supplementary ⇒ ∠3 = 180° – 70° = 110°
∠2 = 70°, ∠3 = 110°

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