RD Sharma 2020 solution class 9 chapter 10 Lines and Angles VSAQS

VSAQS

Page-10.59

Question 1:

Define complementary angles.

Answer 1:

Complementary Angles: Two angles, the sum of whose measures is, are called complementary angles.

Thus, anglesand are complementary angles, if

Example 1:

Angles of measure andare complementary angles, because

Example 2:

Angles of measure andare complementary angles, because

Question 2:

Define supplementary angles.

Answer 2:

Supplementary Angles: Two angles, the sum of whose measures is , are called supplementary angles.

Thus, anglesand are supplementary angles, if

 

Example 1:

Angles of measure andare supplementary angles, because

Example 2:

Angles of measure andare supplementary angles, because

Question 3:

Define adjacent angles.

Answer 3:

Adjacent angles: Two angles are called adjacent angles, if:

1. They have the same vertex,

2. They have a common arm, and

3. Uncommon arms are on either side of the common arm.

In the figure above,and have a common vertex.

Also, they have a common arm and the distinct arms and, lies on the opposite sides of the line.

Therefore, and are adjacent angles.

Question 4:

The complement of an acute angle is ..............

Answer 4:

The complement of an acute angle is an acute angle.

Explanation:

As the sum of the complementary angles is.

Let one of the angle measures.

Then, other angle becomes, which is clearly an acute angle.

Question 5:

The supplement of an acute angle is .................

Answer 5:

The supplement of an acute angle is an obtuse angle.

Explanation:

As the sum of the supplementary angles is.

Let one of the angle measures, such that

Let the other angle measures

As the angles are supplementary there sum is.

Then, other angle y is clearly an obtuse angle.

Illustration:

Let the given acute angle be

Then, the other angle becomes

This is clearly an obtuse angle.

Question 6:

The supplement of a right angle is ..............

Answer 6:

We have to find the supplement of a right angle.

We know that a right angle is equal to.

Let the required angle be.

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

Thus, the require angle becomes

Question 7:

Write the complement of an angle of measure x°.

Answer 7:

We have to write the complement of an angle which measures.

Let the other angle be.

We know that the sum of the complementary angles be 90°.

Therefore,

Question 8:

Write the supplement of an angle of measure 2y°.

Answer 8:

Let the required angle measures

It is given that two angles measuring andare supplementary. Therefore, their sum must be equal to.

Or, we can say that:

Hence, the required angle measures.

Question 9:

If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.

Answer 9:

It is given that the six spokes are equally spaced, thus, two adjacent spokes subtend equal angle at the centre of the wheel.

Let that angle measures

Also, the six spokes form a complete angle, that is,

Therefore,

Hence, the measure of the angle between two adjacent spokes measures.

Question 10:

An angle is equal to its supplement. Determine its measure.

Answer 10:

Let the supplement of the angle be

According the given statement, the required angle is equal to its supplement, therefore, the required angle becomes.

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

Or we can say that:

Hence, the required angle measures .

Question 11:

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

Answer 11:

Let the complement of the required angle measures

Therefore, the required angle becomes

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

Or we can say that :

Hence, the required angle becomes:

Question 12:

How many pairs of adjacent angles are formed when two lines intersect in a point?

Answer 12:

Let us draw the following diagram showing two linesand intersecting at a point.

We have the following pair of adjacent angles, so formed:

and

and

and

and

Hence, in total four pair of adjacent angles are formed.