Assam SCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1

Assam SCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles (Exercise 5.1) | 2025-26 | Download Free PDF

Students can now access SCERT Assam Solutions for Class 7 Maths Chapter 5 – Lines and Angles (Exercise 5.1, English Medium), designed as per the latest syllabus for the 2025-26 academic session. These solutions, prepared by subject experts at Digital Pipal Academy, help students build a strong understanding of angles, intersecting lines, and their properties.

Topics Covered in Exercise 5.1:

✔ Types of angles – Acute, obtuse, right, straight, reflex, and complete angles
✔ Basic properties of lines and angles
✔ Complementary and supplementary angles
✔ Vertically opposite angles and adjacent angles

Key Features of SCERT Assam Class 7 Maths Solutions:

✔ Step-by-step explanations for conceptual clarity
✔ Practice online to strengthen problem-solving skills
✔ Download free PDF for offline study
✔ Exercise-wise solutions to help students score better in exams

SCERT Assam Class 7 Maths Chapter 5 – Lines and Angles (Exercise 5.1)

Click on the link below to access detailed solutions for Exercise 5.1:

 

Q.1. Find out the complementary angles of the following:

(তলত দিয়া কোণবোৰৰ পূৰক কোণৰ মাৰ্প কিমান?)

(a) 45°

(b) 65°

(c) 41°

(d) 54°

Solution:

(a) The complementary angle of 45 ° = 90 ° - 45 ° = 45 °

(b) The complementary angle of 65 ° = 90 ° - 65 ° = 25 °

(c) The complementary angle of 41 ° = 90 ° - 41 ° = 49 °

(d) The complementary angle of 54 ° = 90 ° - 54 ° = 36 °

 

Q.2. If the difference of measures of a pair of complementary angles is 22 °. Find the angles.

[ এযোৰ পূৰক কোণৰ মাপৰ পাৰ্থক্য 22° হ'লে কোণবোৰৰ মাপ নিৰ্ণয় কৰা।]

Solution:

Let the measures of a pair of complementary angles are x ° and 90° - x

According to question,

(90 ° - x)-x =22°

⇒ 90°-x -x = 22 °

⇒-2x = 22° - 90°

⇒ 2x = -68°

⇒x= `\color{purple} {\frac{-68°}{-2}}`

⇒x = 34°

∴ Measures of two complementary angles are 34 ° and (90° - 34 °)=56°

Q.3. Write down the measures of the angles supplementary to each of the following angle.

(তলৰ কোণবোৰৰ প্ৰত্যেকৰে সম্পূৰক কোণৰ মাপবোৰ লিখা।)

(a), 100 °

b) 90°

(c) 55 °

(d) 125 °

Solution:

(a) Supplementary angle of 100° = 180 ° - 100 ° = 80 °

(b) Supplementary angle of 90 ° = 180 ° - 90 ° = 90 °

(c) Supplementary angle of 55 ° = 180 ° - 55 ° = 125 °

(d) Supplementary angle of 125 ° = 180 ° - 125 ° = 55 °

 

Q.4. A pair of supplementary angles is such that the larger angle is 44° more than the smaller angle. Find the measures of the angles.

[এযোৰ সম্পূৰক কোণৰ ডাঙৰ কোণটোৰ মাপ সৰু কোণটোৰ মাপতকৈ 44 ° বেছি। কোণ দুটাৰ মাপ নিৰ্ণয় কৰা।]

Solution:

Let the smaller angle be x.

Since the angles are supplementary, their sum is 180°.

Given that the larger angle is 44° more than the smaller angle.

The larger angle is (x+44°)

According to question,

`x+(x+44°)=180°`

`⇒x+x+44°=180°`

`⇒ 2x=180°-44°`

`⇒2x=136°` 

`⇒x=\frac{136°}{2}`

`⇒x=68°`

Thus, the smaller angle is 68°, and the larger angle is 112°.

 

Q.5. The lines PQ and RS intersect at O. If ∠POR = 50° then find the measures of the other angles.

[ PQ আৰু RS ৰেখা দুডালৰ ছেদবিন্দু O, যদি ∠ POR = 50 ° তেন্তে বাকীবোৰ কোণৰ মাপ নিৰ্ণয় কৰা।]

 

Solution:

Given that ∠ POR = 50°

∴ ∠QOS = 50°        (∵ Vertically opposite angles are equal)

∠ROQ = 180° - 50° = 130° (∵Linear pair angles sum to 180°)

Vertically opposite to ∠ROQ is ∠POS, so ∠POS = 130.

 

Q.6. Find x from the following figure.

[চিত্ৰৰ পৰা নিৰ্ণয় কৰা।]

Solution:

From the given figure, the angles 60°, x, and 45° form a straight line.

Since the sum of angles on a straight line is 180°,

∴We write

60°+ x + 45°= 180°

⇒x + 105° = 180°

⇒x = 180° - 105° = 75°

Q.7. Find an angle which is equal to its supplementary angle.

[এটা কোণ নিৰ্ণয় কৰা যিটো তাৰ সম্পূৰক কোণৰ সমান।]

Solution:

Let the required angle be x. Since the angle is equal to its supplementary angle,

We can write: 

 x + x =180°

⇒ 2x = 180 °

⇒ x = `\frac{180°}{2}`

⇒ x = 90°

The angle that is equal to its supplementary angle is 90°.

Q.8. The measure of an angle is 24°more then its complementary angle. Find the measure of the angle.

[ এটা কোণৰ মাপ তাৰ পূৰক কোণৰ মাপতকৈ 24° বেছি। কোণটোৰ মাপ নির্ণয় কৰা।]

Solution:

Let the complementary angles be x and (x + 24°).

Since the sum of complementary angles is 90°, we write:

 x + x + 24° = 90°

⇒ 2x = 90° - 24°

⇒ 2x =66°

⇒ x = `\frac{66°}{2}`

        = 33°

∴ The angle is 57°.

Q.9. The measure of an angle is 32° less then its complementary angle. Find the measure of the angle.

[এটা কোণৰ মাপ তাৰ পূৰক কোণৰ মাপতকৈ 32° কম। কোণটোৰ মাপ নিৰ্ণয় কৰা।]

Solution:  

Let the complementary angles be x and (x - 32°).

Since the sum of complementary angles is 90°, we can write,

    x + x - 32°= 90°

⇒ 2x = 90 ° + 32 °

 ⇒ 2x = 122°

⇒ x = `\frac{122°}{2}` = 61°

Thus, the required angle is,

`x-32°=61°-32°=29°` 

∴The angle is 29°

Q.10. The measure of an angle is five times the measure of its complementary angle. Find the measure of the angle.

[Q.10. এটা কোণ তাৰ পূৰক কোণৰ পাঁচগুণ। কোণটো নির্ণয় কৰা।]

 

Solution:  

Let the complementary angles be x and 5x.

Since the sum of complementary angles is 90°, we  Can write,

∴  x+5x = 90°

⇒6x=90°

⇒ x = `\frac{90°}{6}`

       = 15°

∴ Thus, the required angle is 5x = 5×15° = 75°

Q.11. An angle is five times the measure of its more than its supplementary angle. Find the measure of the angle.

[Q.11. এটা কোণ তাৰ সম্পূৰক কোণৰ পাঁচগুণ। কোণটোৰ মাপ নির্ণয় কৰা।]

Solution:

Let x be the measure of the angle.

Its supplementary angle is = 180° - x

According to question,

X = 5(180° - x)

⇒x = 900° - 5x

⇒ x+5x = 900°

⇒6x=900°

⇒ x = (900°)/(6)

        = 150°

∴ Thus, the required angle is = 150°

Q.12. The ratio of two supplementary angles is 3: 2. Find the angles.

[Q.12. দুটা সম্পূৰক কোণৰ অনুপাত 3: 2 হ'লে কোণ দুটা নির্ণয় কৰা।]

Solution:  

Let the two supplementary angles be 3x and 2x.

Since supplementary angles sum to 180°, we can write:

3x + 2x = 180 °

⇒ 5x = 180 °

⇒ x = `\frac{180°}{5}`

       = 36 ° 

Thus, the two angles are,

∴ Measure of angles are 2x =2 × 36 ° = 72 ° and

3x=3 × 36 ° = 108 °

Q.13. The ratio of two complementary angles is 4: 5.Find the angles.

[Q.13. দুটা পূৰক কোণৰ অনুপাত 4: 5 হ'লে কোণ দুটা নিৰ্ণয় কৰা।]

Solution: 

Let the two complementary angles be 4x and 5x.

Since complementary angles sum to 90°, we can write,

4x + 5x = 90 °

⇒ 9x = 90 °

⇒ x = `\frac{90°}{9}` = 10°

 ∴ Two angles are 4× 10 ° = 40 ° and 5×10 ° = 50 °

Q.14. Find x and y from the following diagrams.

[Q.14. তলৰ চিত্ৰ দুটাৰ পৰা x আৰু y নিৰ্ণয় কৰা।]

Solution: (a)

Given ∠40° in the diagram. Since x and 40° are alternate interior angles, we get:

$$x = 40°$$

Since x and y are supplementary (they form a linear pair), we can write:

$$x + y = 180°$$ $$40° + y = 180°$$ $$y = 140°$$

Thus, x = 40°, y = 140°.

Solution  (b)

Given ∠55° and a right angle (90°).
Since the sum of angles on a straight line is 180°, we can write:

$$x + 90° + 55° = 180°$$ $$x + 145° = 180°$$ $$x = 35°$$

Q.15. Identify the pairs of complementary angles from the following.

(তলৰ কোণৰ যোৰবোৰৰ পৰা পূৰক কোণৰ যোৰবোৰ চিনাক্ত)

(a) 65 ° ,25 °

(b) 63 °, 27 °

(c) 112 ° ,68 °

(d) 130 °, 50 °

Solution: 

Complementary angles are two angles whose sum is 90°.

Now, checking each pair:

(a) 65° + 25° = 90° ✅ (Complementary)
(b) 63° + 27° = 90° ✅ (Complementary)
(c) 112° + 68° = 180° ❌ (Not Complementary)
(d) 130° + 50° = 180° ❌ (Not Complementary)

The pairs of complementary angles are (a) 65° , 25° and (b) 63° , 27°.

Q.16. Identify the pairs of supplementary angles from the following.

(তলৰ কোণৰ যোৰবোৰৰ পৰা সম্পূৰক কোণৰ যোৰবোৰ চিনাক্ত কৰা)

(a) 110 °, 70 °

(b) 163 °, 27 °

(e) 112 °, 68 °

(d) 45 ° ,45 °

Solution:

Supplementary angles are two angles whose sum is 180°.

Now, checking each pair:

(a) 110° + 70° = 180° ✅ (Supplementary)
(b) 163° + 27° = 190° ❌ (Not Supplementary)
(c) 112° + 68° = 180° ✅ (Supplementary)
(d) 45° + 45° = 90° ❌ (Not Supplementary)

The pairs of supplementary angles are (a) 110° , 70° and (c) 112° , 68°.

Question: Identify the following pairs of lines as parallel, intersecting perpendicularly or intersecting lines.[ তলৰ ৰেখা কেইযোৰ সমান্তৰাল, নে পৰস্পৰ লম্ভভাবে কটাকটি কৰা, নে কটাকটি কৰা চিনাক্ত কৰা।)

 

Ans. Parallel lines: (i), (v)

Intersecting perpendicularly lines: (ii), (iv)

Intersecting lines: (iii), (iv)

উত্তৰ। সমান্তৰাল ৰেখা: (i), (v)

পৰস্পৰ লম্বভাৱে কটাকটি কৰা ৰেখা: (ii), (vi)

কটাকটি কৰা ৰেখা: (iii), (iv) 

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