SEBA Class 7 Mathematics Chapter 5 Lines and Angles

SEBA Class 7 Mathematics Chapter 5 Lines and Angles Solutions English Medium, SEBA Class 7 Maths Notes in English Medium, SEBA Class 7 Mathematics Chapter 5 Lines and Angles Notes to each chapter is provided in the list so that you can easily browse throughout different chapter Assam Board SEBA Class 7 Mathematics Chapter 5 Lines and Angles Solutions in English and select needs one.

SEBA Class 7 Mathematics Chapter 5 Lines and Angles

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Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 7 General Maths Textual Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 7 Mathematics Chapter 5 Lines and Angles Solutions for All Subject, You can practice these here.

Lines and Angles

Chapter – 5

1. Find out the complementary angles of the following:

(a) 45°

Ans: The complementary angle of (90° – 45°) = 45°

(b) 65°

Ans: The complementary angle of (90° – 65°) = 25°

(c) 41°

Ans: The complementary angle of (90° – 41°) = 49°

(d) 54°

Ans: The complementary angle of (90°- 45°) = 36°

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

Ans: Let the measure of a pair of complementary angles are x° and 90° – x

∴ A/Q, x – (90° – x) = 22°

⇒ x – 90° + x = 22°

⇒ 2x =  22° + 90°

⇒ 2x = 112°

 ⇒ x = 112°/2 = 56°

∴ Measure of two complementary angles are 56° and (90° –  56°) = 34°

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

(a) 100°

Ans: 180° – 100° = 80°

(b) 90°

Ans: 180° – 90° = 90°

(c) 55°

Ans: 180° – 55° = 125°

(d) 125°

Ans: 180° – 125° = 55°

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.

Ans: Let the larger angle of a pair of supplementary angles x° and the smaller angle = 180 ° – x°

∴ A/Q, x° = 180° – x° + 44°

⇒ 2x° = 224°

⇒ x° = (224°)/2 

 ⇒ x° = 112°

 ∴ Larger angle = 112° and smaller angle = 180° – 112° = 68°

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

Ans: ∠POR = 50° 

∴ ∠SOQ = 50° 

∠POR = ∠POS = 180°

⇒ 50° + ∠POS = 180° 

⇒ ∠POS = 180°- 50° = 130° 

∴ ∠ROQ = 130°

6. Find x from the following figure.

Ans: 60° + x + 45° = 180° (straight angle)

⇒ 105° + x = 180°

⇒ x = 180° – 105° = 75°

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

Ans: Let the two angles be x and x 

∴ x + x = 180°

⇒ 2x = 180° 

⇒ x = (180°)/2 

⇒ x = 90°

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

Ans: Let the two complementary angles be x and x

∴ x + x + 24° = 90°

⇒ 2x = 90° – 24° 

⇒ 2x = 66°

⇒ x = (66°)/2

= 33°

∴ Two angles are 33° and 33° + 24° = 57°

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

Ans: Let the two complementary angles are x and x – 32° x + x – 32° = 90°

⇒ 2x = 90° + 32°

⇒ 2x = 122°

⇒ x = (122°)/2 = 61°

∴ Measure of the angles are 61° and (61° – 32°) = 29°

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

Ans: Let the two complementary angles are x and 5x. 

∴  x + 5x = 90° 

⇒ 6x = 90° 

⇒ x = (90°)/6 

= 15°

∴ The measure of the angle = 5 × 15° = 75°

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

Ans: Let the two angles are x and 5x. x + 5x = 180° 

⇒ 6x = 180°

⇒  x  = (180°)/6

= 30°

∴ The measure of the angle

 = 5 × 30° = 150°

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

Ans: Let the two supplementary angles are 3x & 2x.

∴ 3x + 2x = 180

⇒ 5x = 180 

⇒ x = 36

∴ Measure of angles are = 3 × 36° = 180° and 2 × 36° = 72°

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

Ans: Let the two angles are 4x and 5x 

∴ 4x + 5x = 90° 

⇒ 9x = 90° 

⇒ x = (90°)/9 = 10°

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

14. Find x and y from the following diagrams.

(a) 

Ans: x = 40° [Vertically opp. angels]

x + y = 180° 

⇒ 40 + y = 180

⇒ y = 180 – 40 = 140

(b) 

Ans: x = 90° – 55° = 35°

⇒ x = 90° – 55° = 35°

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

(a) 65°, 25°

(b) 63°, 27°

(c) 112°, 68°

(d) 130°, 50° 

Ans: (a) 65°, 25° and (b) 63°, 27°

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

(a) 110°, 70°

(b) 163°, 270

(c) 112°, 68°

(d) 45°, 45°

Ans (a) 110°, 70° and (c) 112°, 68°

1. In the following figure if AB || CD, find x, y and z.

Ans: ∠x = 70° (Alternate angle)

∠y = 180° – (70° + 80°) = 180° – 150° = 30°

∴ ∠z = 180° – (70° + 30°) = 180° – 100° = 80° 

x = 70°

y = 30°

z = 80°

Ans: x = 30° + 180° – 65° = 180°

⇒ x = 65° – 30° 

= 35°

Ans: x = 80° (Alternate angle) 

z = 40°

∴ y = 180° – (80° – 40°) 

= 180° – 120° 

= 60°

(d)

Ans: ∠BFD = 55° 

∠BFD = 180° – (55° + 25°) 

= 180°- 80° = 100° 

∴ x = 180° – 100° 

= 80°

2. In the following figures, I and m are two lines and n is a transversal. Find the pair of lines which are parallel to each other?

Ans: (a) and (d)

3. From the figure find given below the measure of x.

Ans: x = 360° – (45° + 30°)

= 360° – 75° = 285°

4. In the figure given below 1 || m, t is transversal. Find the value of x.

Ans: x = 120°[ corresponding angle]

Ans: x = 180° – 60° = 120° x = 60°

Ans:  x =  60° [alternate angle]

Q.1. If a pair of adjacent angles are supplementary to each other, then they will form-

(a) corresponding angles.

(b) vertically opposite angles.

(c) linear pair of angles.

(d) a ray.

Ans. (c) linear pair of angles.

Q.2. If two angles are supplementary their sum will be-

(a) 90°

(b) 180°

(c) 360°

(d) 45°

Ans. (b) 180°

Q.3. If two angles are complementary to each other, their sum will be-

(a) 45°

(b) 180°

(c) 90°

(d) 360°

Ans. (c) 90°

4. In the adjoining figure if l ||m then ∠1 = ∠2 since they are-

(a) corresponding angles.

(b) vertically opposite angles.

(c) alternate interior angles.

(d) supplementary angles.

Ans: (c) alternate interior angles.

5. In the figure the pair of alternate interior angles will be.

(a) ∠1, ∠3

(b) ∠2, ∠3

(c) ∠2, ∠5

(d) ∠2, ∠4

Ans: (b) ∠2, ∠3

6. If a || b and c is a transversal, then angle y is-

(a) 90°

(b) 125°

(c) 55°

(d) 180°

Ans: (c) 55°

7. If a || b and c is a transversal, then Zy is-

(a) 90°

(b) 25°

(c) 55°

(d) 35°

Ans: (c) 55°

8. The measure of the complementary angle of 45° is-

(a) 135°

(b) 25°

(c) 35°

(d) 45°

Ans: (d) 45°

9. Which of the following angles will be equal to its own complementary angle?

(a) 30°

(b) 25°

(c) 35°

(d) 45°

Ans: (d) 45°

10. Which of the following angles will be equal to its own supplementary angle?

(a) 60°

(b) 90°

(c) 180°

(d) Non of the above.

Ans: (b) 90°

11. If 1 || m and c is the transversal then x is-

(a) 30°

(b) 60°

(c) 90°

(d) 180°

Ans: (b) 60°

12. In the given figure 1 || m and c is transversal. The value of x is-

(a) 50°

(b) 130°

(c) 120°

(d) 100°

Ans: (b) 130°

13. In the given figure 1 || m and c is transversal. The value of x is-

(a) 10°

(b) 20°

(c) 30°

(d) 25°

Ans: (b) 20°

14. If two lines are equidistant from each other then they are-

(a) perpendicular lines.

(b) non parallel lines.

(c) Intersecting lines.

(d) parallel lines.

Ans. (d) parallel lines.

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