CBSE Class 6 Maths (Ganita Prakash) Important Questions Chapter 2 - Lines and Angles

1. What is the name of an angle that measures exactly 90°?

Ans: An angle that measures exactly 90° is called a right angle.

2. Identify the type of angle if it measures between 90° and 180°.

Ans: An angle that measures between 90° and 180° is called an obtuse angle.

3. How many degrees are there in a complete rotation around a point?

Ans: A complete rotation around a point measures 360°.

4. What is the sum of two complementary angles if one of the angles is 35°?
Ans: The sum of complementary angles is always 90°.
Let the other angle be xxx.
So, x + 35° = 90°
x = 90° − 35° = 55°
Therefore, the other angle is 55°.

5. What is the measure of each angle if two angles are supplementary and one of them is 110°?
Ans: The sum of supplementary angles is always 180°.
Let the other angle be y.
So, y + 110° = 180°
y = 180° − 110° = 70°
Therefore, the other angle is 70°.

6. Two angles are vertically opposite. If one of the angles is 45°, what is the measure of the other angle?
Ans: Vertically opposite angles are equal.
So, if one angle is 45°, the other vertically opposite angle is also 45°.

7. Define adjacent angles.

Ans: Adjacent angles are two angles that have a common vertex and common arm but do not overlap. They lie next to each other.

8. Find the angle measure if an angle is twice its complement.
Ans: Let the angle be xxx and its complement be 90° − x
According to the question, x =2 $\times$ (90° - x)
Solving:
x = 180° − 2x
3x = 180° 

x = 60°

So, the angle is 60°, and its complement is 30°.

9. What is the measure of each angle if two angles are complementary and equal?

Ans: Let each angle be x. Since they are complementary, x + x = 90°.

So, 2x = 90°, x = 45°.

Therefore, each angle measures 45°.

10. If two angles are in the ratio 2:3 and are supplementary, find the measures of the angles.
Ans: Let the angles be 2x and 3x.
Since they are supplementary, 2x + 3x = 180°
5x = 180°
x = 36°
The angles are 2x = 2 $\times$ 36° = 72° and 3x = 3 $\times$ 36° = 108°.
So, the angles are 72° and 108°.

11. An angle is 30° less than its supplement. Find the angles.
Ans: Let the angle be xxx and its supplement be 180° − x.
According to the question, x = (180° − x) − 30°.
Solving:
x + x = 150°
2x = 150°
x = 75°
So, one angle is 75° and the other is 180° − 75° = 105°.
The angles are 75° and 105°.

12. If one angle of a linear pair is 75°, what is the measure of the other angle?

Ans: In a linear pair, the sum of the angles is 180°.

So, the other angle is 180° − 75° = 105°.

Thus, the measure of the other angle is 105°.

13. Find the angle which is equal to its own complement.
Ans: Let the angle be x.
Since it’s equal to its complement, x + x = 90°.
2x = 90°
x = 45°
So, the angle is 45°.

14. If two lines intersect and one of the angles formed is 120°, what are the measures of the other three angles?
Ans: When two lines intersect, they form two pairs of vertically opposite angles.
If one of the angles is 120°, the angle vertically opposite to it is also 120°.
The other two angles are supplementary to 120°, so each will be 180° − 120° = 60°.
Thus, the four angles are 120°, 120°, 60°, and 60°.

15. If two angles are supplementary and one of them is 35° more than the other, find the angles.

Ans: Let the smaller angle be x; the larger angle is x + 35°.

Since they are supplementary:

x + (x+35°) = 180°

2x = 145°

x = 72.5° 

Therefore, x + 35° = 72.5° + 35°  = 107.5°

The angles are 72.5° and 107.5°.

16. An angle is 40° more than its complement. Find the angles.
Ans: Let the angle be xxx and its complement be 90° − x.
According to the question, x = (90°−x) + 40°.
Solving:
2x=130°2x = 130°2x=130°
x=65°x = 65°x=65°
So, the angle is 65° and its complement is 90°−65°=25°90° - 65° = 25°90°−65°=25°.
The angles are 65° and 25°.

17. Name an example of perpendicular lines in daily life.

Ans: An example of perpendicular lines in daily life is the intersection of the edges of a notebook (where the horizontal and vertical edges meet at right angles).

18. Find the angles if two angles are in the ratio 3:7 and are supplementary.
Ans: Let the angles be 3x and 7x.
Since they are supplementary, 3x + 7x = 180°.
10x = 180°

x =18°
The angles are 3x = $ \times$ 18° = 54° and 7x = 7$ \times $18° = 126°.
So, the angles are 54° and 126°.

19. What is the measure of the angle formed by the hands of a clock at 3 o’clock?

Ans: At 3 o’clock, the minute hand is at 12, and the hour hand is at 3, forming a right angle.

Therefore, the angle formed is 90°.

20. If two angles are in the ratio 4:5 and form a linear pair, find the measures of the angles.

Ans: Let the angles be 4x4x4x and 5x5x5x. Since they form a linear pair, their sum is 180°.

So, 4x + 5x = 180°

9x = 180°

x = 20°

The angles are 4x = 4 $\times $20° = 80° and 5x = 5 $\times $20° = 100°.

Thus, the angles are 80° and 100°.

Solve Extra Questions to Improve Your Marks

1. In Fig. below name:

(a) Five points
(b) Aline
(c) Four rays
(d) Five line segments
Answer:
(a) Points B, C, D, E and O.
(b) Line: DB
(c) Rays: $\overrightarrow{\mathrm{OB}}$ , $\overrightarrow{\mathrm{OC}}$ , $\overrightarrow{\mathrm{OD}}$ ; $\overrightarrow{\mathrm{OE}}$
(d) Line segments: DE, EO, OB, DC, DO.

2. Explain why ∠APC cannot be labelled as ∠P.

Answer:
Sol. At P there are three angles.
∠P could mean ∠APB or ∠BPC or ∠APC.
To get the correct angle, it has to be named as ∠APC or ∠APB or ∠BPC.
Also, note that a single point can not form an angle.

3. In each case, determine which angle- is greater and why.

(a) ∠AOB or ∠XOY
(b) ∠AOB or ∠XOB
(c) ∠XOB or ∠XOC
Discuss with your friends on how you decided which one is greater.
Answer:
(a) ∠AOB > ∠XOY
(∠AOB has more spread than ∠XOY)

(b) ∠AOB > ∠XOB
(∠AOB has more spread than ∠XOB)

(c) ∠XOB = ∠XOC
(B and C are points on the same ray; both angles have the same arms and vertex, hence the same spread)

4. Make a few acute angles and a few obtuse angles. Draw them in different orientations.
Answer:

5. Estimate the size of each angle and then measure it with a protractor:

Classify these angles as acute, right, obtuse or reflex angles.
Answer:
(a) 45° acute
(b) 150° obtuse
(c) 120° obtuse
(d) 30° acute
(e) 95° obtuse
(f) 350° reflex

5 Important Formulas Points of Class 6 Chapter 2 You Shouldn’t Miss!

This page is all about the important questions from CBSE Class 6 Maths Chapter 2 - Lines and Angles that you need to practice. These short question answers are specially designed to help you understand the concepts better.

You will also find some extra questions with answers which will help you in your thorough revision and also to perform well in your test paper.

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