RD Sharma 2020 solution class 9 chapter 10 Lines and Angles Exercise 10.1

Exercise 10.1

Page-10.7

Question 1:

Write the complement of each of the following angles:

(i) 20°

(ii) 35°

(iii) 90°

(iv) 77°

(v) 30°

Answer 1:

(i) Let the complement of angle measures x°

Since the angles are complementary, therefore their sum must be equal to

Or we can say that

Hence, the complement of angle measures

(ii) Let the complement of angle measures x°

Since the angles are complementary, therefore their sum must be equal to

Or we can say that

Hence, the complement of angle measures

(iii) Let the complement of angle measures x°

Since the angles are complementary, therefore their sum must be equal to

Or we can say that

Hence, the complement of angle measures

(iv) Let the complement of angle measures x°

Since the angles are complementary, therefore their sum must be equal to

Or we can say that

Hence, the complement of angle measures

(v) Let the complement of angle measures x°

Since the angles are complementary, therefore their sum must be equal to

Or we can say that

Hence, the complement of angle measures.

Question 2:

Write the supplement of each of the following angles:

(i) 54°

(ii) 132°

(iii) 138°

Answer 2:

(i) Let the supplement of angle measures x°

Since the angles are supplementary, therefore their sum must be equal to

Or we can say that

Hence, the supplement of angle measures.

(ii) Let the supplement of angle measures x°

Since the angles are supplementary, therefore their sum must be equal to

Or we can say that

Hence, the supplement of angle measures.

(iii) Let the supplement of angle measures x°

Since the angles are supplementary, therefore their sum must be equal to

Or we can say that

Hence, the supplement of angle measures.

Question 3:

If an angle is 28° less than its complement, find its measure.

Answer 3:

Let one angle be x°.

Then the required angle becomes

It is given that x° andare complementary

Therefore their sum must be equal to

On dividing both sides of the equation by 2,we get:

Also

Hence the measure of the required angle is.

Question 4:

If an angle is 30° more than one half of its complement, find the measure of the angle.

Answer 4:

Let the measure of the required angle be x°.

Thus its complement becomes

According to the statement, the required angle is 30 more than half of its complementary angle that is; the required angle x becomes,

.

Thus

Taking 2 on left hand side of the equation, we get

Hence, the required angle measures.

Question 5:

Two supplementary angles are in the ratio 4:5. Find the angles.

Answer 5:

Let the two angles be 4x and 5x.

Since the angles are given as supplementary, therefore their sum must be equal to

This can also be written as

Dividing both sides of equation by 9, we get

The two angles become

Also,

Hence,and are the measure of two supplementary angles.

Question 6:

Two supplementary angles differ by 48°. Find the angles.

Answer 6:

Let one angle measures. Then, the second angle becomes.

Since the angles are supplementary, therefore their sum must be equal to.

Thus,

On dividing both sides of the equation by, we get

Also,

Hence, the required angles measureand.

Question 7:

An angle is equal to 8 times its complement. Determine its measure.

Answer 7:

Let the required angle be x°

Thus its complement becomes

It is given that the angle x is 8 times its complementary angle, this means

Hence, the required angle measures.

Question 8:

If the angles (2x − 10)° and (x − 5)° are complementary angles, find x.

Answer 8:

It is given that and are complementary angles.

Therefore, their sum must be equal to 90°.

Thus,

Hence the value of x is.

Question 9:

If an angle differs from its complement by 10°, find the angle.

Answer 9:

Let the angle measures x°

Therefore, the measure of its complement becomes

According to the question the above mentioned complementary angles differ by 10°.

Thus,

Hence the required angle measures.

Question 10:

If the supplement of an angle is two-third of itself. Determine the angle and its supplement.

Answer 10:

Let the angle measures x°.

Therefore, the measure of its supplement is

It is given that the supplement is two third of itself, this means

Now, let’s calculate the supplement

Hence, the measure of the angle and its supplement areandrespectively.

Question 11:

An angle is 14° more than its complementary angle. What is its measure?

Answer 11:

Let the angle measures x°

Therefore, the measure of its complement becomes

According to the given statement, the angle is 14 more than its complement.

Thus we have,

The measure of its complement becomes

Hence, the required angle measures and its complement measures.

Question 12:

The measure of an angle is twice the measure of its supplementary angle. Find its measure.

Answer 12:

Let the angle measures x°

Therefore, the measure of its supplement becomes

According to the given statement, the required angle is twice the supplement.

Thus

Hence the required angle measures.

Question 13:

If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

Answer 13:

Let the angle measures x°

Therefore, the measure of its complementary angle becomes

Also, supplement of its thrice means

According to the question,

Hence, the required angle measures.

Question 14:

If the supplement of an angle is three times its complement, find the angle.

Answer 14:

Let the angle measures x°

Therefore, the measure of its complement isand measure of its supplement is

According to the question the supplement of is three times the complement, this means

Hence, the required angle measures.