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#### Chapter 6: Lines and Angles

2 Marks Questions

1. In the given figure, if ∠COA = 62°, then find x.

Sol. x + 62° = 180° [Since, AOB is a line]

⇒ x = 180° – 62° = 118°.

2. In the given figure, find the value of x.

Sol. 4x + 2x + x + 150° = 360°

[Since, all angles given on same point]

⇒ 7x + 150° = 360° ⇒ 7x = 210° ⇒ x = 30°

3. In the given figure, find the value of x.

Sol. By vertically opposite angles, and the sum of all the angles on the same side of a line is 180°.

⇒ 3x + 4x + 2x = 180° ⇒ 9x = 180° ⇒ x = 20°.

4. In the given figure, find the value of x.

Sol. Since, AOB is a straight line.

⇒ 45° + 2x + x + 15° = 180°

⇒ 3x + 60° = 180° ⇒ 3x = 120°

⇒ x = 40°

5. In the given figure, find ∠ACD.

Sol. 6x + 40° + 4x = 180° [since, ACB is a straight line]

⇒ 10x = 180° – 40° = 140° ⇒ x = 14°

6. Find the angle which is two times its supplement.

Sol. Let the angle is x°, then its supplement is 180° – x.

∴ x = 2 (180° – x)

⇒ x = 360° – 2x ⇒ 3x = 360°

⇒ x = 120°.

7. In the given figure, find the value of x.

Sol. 3x + 2x + 30 = 180°

[Since, all angles given on a line]

⇒ 5x + 30° = 180° ⇒ x = 30°

8. In the given figure, AOB is a straight line. Find ∠x + ∠y + ∠z + ∠w.

Sol. Since AOB is a straight line, therefore the sum of all the angles makes on it will be 180°.

9. Find the value of x in the figure.

Sol. x° + 55° + (2x + 5°) = 180°

[since, AOB is a straight line]

⇒ 3x + 60° = 180° ⇒ 3x = 120° ⇒ x = 40°

10. Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle ? Justify your answer.

Sol. No. Each of these angles will be a right angle only when they form a linear pair.

11. In the figure, POQ is a line. Find the value of x.

Sol. 40° + 4x° + 3x° = 180°

12. In the given figure find the value of x so that POQ is a straight line.

Sol. Since POQ is a straight line

∴ 2x + 30 + 4x = 180°

⇒ 6x = 150 ⇒ x = 25

13. In the given figure, find the value of x.

Sol. We know that the sum of all the angles around a point is equal to 360°.

∴ x + x + 10° + 120° = 360°

⇒ 2x + 130° = 360°

⇒ x = 115°.

14. Find the angle which is equal to 8 times its complement.

Sol. Let the angle is x°, then its complement is 90° – x

∴ x = 8 (90° – x)

⇒ x = 720° – 8x

⇒ 9x = 720° ⇒ x = 80°

15. In figure, AOB is a straight line. Find the value of x

Sol. Since AOB is a straight line.

30° + 90° + 2x = 180°

⇒ 2x = 180° – 120° ⇒ x = 30°

16. In the figure, AOB is a straight line. Find the measure of ∠COD.

Sol. x + 20° + 2x – 20° + 60° = 180° [Since AOB is a straight line]

⇒ 3x = 180° – 60° = 120° ⇒ x = 40°

∴ ∠COD = 2 (40) – 20 = 60°.
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