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 twothird 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°]
1 videos228 docs21 tests

1. What are the types of angles discussed in Chapter 6 of Class 9 Maths? 
2. How can we identify parallel lines? 
3. What is the difference between a line segment and a ray? 
4. How many degrees are there in a straight angle? 
5. What is the difference between complementary and supplementary angles? 
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