Lines and Angles Questions
Chapter – Lines and Angles
Class 9th HP Board Mathematics
Q1. What is a line?
Solution:
A line is a straight path that extends endlessly in both directions. It has no endpoints.
Q2. What is a line segment?
Solution:
A line segment is a part of a line that has two fixed endpoints and a definite length.
Q3. Define a ray.
Solution:
A ray is a part of a line that has one fixed endpoint and extends endlessly in one direction.
Q4. What are complementary angles?
Solution:
Two angles whose sum is 90° are called complementary angles.
Example: 30° and 60° are complementary angles.
Q5. What are supplementary angles?
Solution:
Two angles whose sum is 180° are called supplementary angles.
Example: 110° and 70° are supplementary angles.
Q6. What are adjacent angles?
Solution:
Two angles are called adjacent angles if they have a common vertex, a common arm and their interiors do not overlap.
Q7. What are vertically opposite angles?
Solution:
When two straight lines intersect each other, the opposite angles formed are called vertically opposite angles. These angles are always equal.
Q8. If one angle of a linear pair is 65°, find the other angle.
Solution:
We know that the sum of angles in a linear pair is 180°.
Let the other angle be x.
x + 65° = 180°
x = 180° − 65°
x = 115°
Therefore, the other angle is 115°.
Q9. Two lines intersect each other. If one angle is 75°, find its vertically opposite angle.
Solution:
We know that vertically opposite angles are equal.
Therefore, the vertically opposite angle is 75°.
Q10. If two complementary angles are in the ratio 2 : 3, find both angles.
Solution:
Let the two angles be 2x and 3x.
Since they are complementary angles:
2x + 3x = 90°
5x = 90°
x = 90°/5
x = 18°
First angle = 2x = 2 × 18° = 36°
Second angle = 3x = 3 × 18° = 54°
Therefore, the two angles are 36° and 54°.