Chapter 6 - Lines and Angles, Solved Examples, Class 9, Maths

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

Ex 1. In figure, AOC = 50° and BOC = 20°, find AOB.
Sol.

Ex 2. In figure,  AOB = 35°, find the reflex  AOB.

Sol.

Ex 3. In figure, OB  OA. AOC and BOC are complementary angles. Find the value of x and
hence find AOC and BOC.

Sol.

Now, AOC = (25 + 10)° = 35° and BOC = {2 × 25 + 5}° = 55°

Ex 4. In figure, ray AD stands on the line CB,  BAD = (2x + 10)° and  CAD = (5x + 30)°, find
the value of x and also write
Sol.

Ex 5. In figure, ray OC stands on the line AB and BOC = 125°. Find reflex AOC.

Sol.

⇒ AOC = 180° – 125° = 55°             (  BOC = 125°)

Now, Reflex  AOC = 360° –  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°

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°.
These angles are supplementary.  3x° + 7x° = 180°
⇒ 10x° = 180°

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 AOC = 4x and BOC = (6x + 30°)?
Sol
. If AOB is a line, then
AOB = 180° [ A straight angle = 180°]

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.
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## Extra Documents & Tests for 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.

## Extra Documents & Tests for Class 9

1 videos|228 docs|21 tests

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