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Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 PDF Download

Ex 1. In figure, Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOC = 50° and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9BOC = 20°, find Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOB.
Sol.

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9


Ex 2. In figure, Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 AOB = 35°, find the reflex Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 AOB.
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

Sol.

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9


Ex 3. In figure, OB Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 OA. Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOC and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9BOC are complementary angles. Find the value of x and
 hence find Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOC and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9BOC.

Sol.

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9
Now, Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 AOC = (25 + 10)° = 35° and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 BOC = {2 × 25 + 5}° = 55°

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9


Ex 4. In figure, ray AD stands on the line CB, Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 BAD = (2x + 10)° and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 CAD = (5x + 30)°, find
 the value of x and also write 
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 BAD and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 CAD.
 Sol.

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9



Ex 5. In figure, ray OC stands on the line AB and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9BOC = 125°. Find reflex Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOC.
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9
 

Sol.

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

⇒ Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOC = 180° – 125° = 55°             ( Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9BOC = 125°)

Now, Reflex Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 AOC = 360° – Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 AOC = 360° – 55° = 305°

 

Ex 6. Find the measure of the complementary angle of the following angles :
 (i) 22°` 

(ii) 63°
Sol. We know that the measure of the complementary angle of x° is equal to (90° – x°). Hence,
(i) Measure of the complementary angle of 22°
= 90° – 22° = 68°
(ii) Measure of the complementary angle of 63°
= 90° – 63° = 27°


Ex 7. How many degrees are there in an angle which equals two-third of its complement?
 Sol. 
Let the required angle be x°.
Then, its complementary angle = 90° – x°
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

Hence, there are 36 degrees in such an angle.


Ex 8. Find the measure of the supplementary angle of the following angles :
 (i) 45°` 

(ii) 57°

Sol. We know that the measure of the supplementary angle of x° is equal to (180° – x°). Hence,
(i) Measure of the supplementary angle of 45°
= 180° – 45° = 135°
(ii) Measure of the supplementary angle of 57°
= 180° – 57° = 123°


Ex 9. Two supplementary angles are in the ratio of 3 : 7. Find the angles.
 Sol. 
Let the two angles in the ratio of 3 : 7 be 3x° and 7x°.
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 These angles are supplementary. Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 3x° + 7x° = 180°
⇒ 10x° = 180°

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9
Hence, the angles are 3x° = 3 × 18° = 54° and 7x° = 7 × 18° = 126°.


Ex 10. What value of x would make AOB a line in figure, if Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOC = 4x and Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9BOC = (6x + 30°)?
 Sol
. If AOB is a line, then
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9AOB = 180° [Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 A straight angle = 180°] 

Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9
Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9

The document Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
All you need of Class 9 at this link: Class 9
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FAQs on Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths - Extra Documents & Tests for Class 9

1. What are the types of angles discussed in Chapter 6 of Class 9 Maths?
Ans. Chapter 6 of Class 9 Maths discusses three types of angles: Acute Angle, Right Angle, and Obtuse Angle.
2. How can we identify parallel lines?
Ans. Two lines are said to be parallel if they never intersect each other. They can be identified based on the following properties: - They have the same slope. - They are equidistant at all points. - They have the same angle of inclination.
3. What is the difference between a line segment and a ray?
Ans. A line segment is a part of a line that has two endpoints. On the other hand, a ray is a part of a line that has one endpoint and extends infinitely in one direction.
4. How many degrees are there in a straight angle?
Ans. A straight angle is a line that measures exactly 180 degrees.
5. What is the difference between complementary and supplementary angles?
Ans. Complementary angles are two angles that add up to 90 degrees, while supplementary angles are two angles that add up to 180 degrees.
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