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Lines and Angles CBSE Class 9

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Question 1/20

Q 1. Two unequal angles of a rhombus are in the ratio 3:2. Find the smallest angle.

Solution

Let the angles be 3x and 2x.

According to the question,

3x + 2x = 180° 

5x = 180° 

x = 36° 

Hence, the angles are 36° × 3 = 108° 

and 36° × 2 = 72°. 

Q 2. If the angles x, y, z form a straight line and  , then the value of y is 

Solution

According to the question,

x + y + z = 180° 

3y + y + 5y = 180° 

9y = 180˚

y = 20˚ 

Q 3. If one of the co-interior angles made by a transversal on a pair of lines is 67°, then the other is

Solution

If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are supplementary.

Q 4. If angles forming a linear pair are equal, then each of these angle is 

Solution

If angles forming a linear pair are equal, then each of these angle is  . 

Q 5. If each of the two lines is perpendicular to the same line, then the lines are

Solution

If each of the two lines is perpendicular to the same line, then the lines are parallel and on the same line.

Q 6. Two unequal angles of a parallelogram are in the ratio 3:6. Find the difference between the angles.

Solution

Let the angles be 3x and 6x.

According to the question,

3x + 6x = 180° 

9x = 180° 

x = 20° 

3x = 3 × 20° = 60° 

6x = 6 × 20° = 120° 

Difference between the angles is 60°. 

Q 7. Which of the following angles are alternate angles if the lines are parallel?   

Solution

2 and 6 are alternate angles. 

Q 8. If 2 = x + 60° and 3 = 4x + 20°, then find the value of x if the lines are parallel.   

Solution

From the figure, the given angles are corresponding angles.

x + 60° + 4x + 20° = 180° 

 5x = 180° - 80° 

5x = 100° 

x = 20° 

Q 9. If the measure of one angle is equal to the complementary of the same angle, then the angle is 

Solution

Let the angle be x.

According to the question,

x = 90° x

2x = 90° 

x = 45° 

Q 10. If a transversal intersects two lines such that the pair of interior angles on the same side of the transversal is supplementary, then the lines are

Solution

If a transversal intersects two lines such that the pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel. 

Q 11. If two lines intersect, then may be they are 

Solution

If two lines intersect, then they are perpendicular and in the same plane. 

Q 12. If a transversal is perpendicular to both parallel lines, then 

Solution

A, B and C are correct.

   

From the figure, all the angles are equal.

 

Q 13. If two straight lines are perpendicular to the same line, then they are ____ to each other. 

Solution

If two straight lines are perpendicular to the same line, then they are parallel to each other. 

Q 14. From the figure, 3 and 5 angles are ____ if the lines are parallel.   

Solution

3 and 5 angles are alternate angles.

Q 15. Find the value of x.   

Solution

From the figure, the angles are complementary.

x + x + 40° = 90° 

2x = 50° 

x = 25° 

Q 16. The supplementary of an obtuse angle is a/an 

Solution

The supplementary of an obtuse angle is an acute angle. 

Q 17. Find the value of x.   

Solution

From the figure, the angles are vertically opposite. Hence,

x - 30 = 4x + 60

4x - x = 30 + 60

3x = 30

x = 10 

Q 18. Find the value of x.   

Solution

From the figure, the interior angles are supplementary.

x + 3x - 40° = 180° 

4x = 180° + 40° 

4x = 220° 

x = 55° 

Q 19. If a transversal intersects two parallel lines, then each pair of

Solution

A, B and C are correct. 

Q 20. Find the value of x.   

Solution

From the figure, the sum of the angles is 180°.

x + 30° + 40° = 180° 

x = 180° 70° 

x = 110° 

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