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  BAD and  CAD.
 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°]