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Chapter 9: Q12. (page 342)

Use a compass to draw a large ⊙o.Draw a central ∠AOB..

a. draw three other points P,Qand R that are on ⊙obut not on ABÁåœ.

then draw ∠APB,∠AQB and ∠ARB.

b. Use a protractor to find m∠AOB,m∠APB,m∠AQB and m∠ARB.

c. What is the relationship between m∠APB,m∠AQB and m∠ARB?

What is the relationship between m∠AOBand m∠APB?

Short Answer

Expert verified

(a)

The final answer is

(b)

The final answeris

∠APB=∠AQB=∠ARB=29∘

(c)

The final answeris all are equal.

∠APB=∠AQB=∠ARB=29∘

There is no such relation between ∠AOBand ∠APB.

Step by step solution

01

Step 1. Given information:

Draw a circle ⊙oand draw a central angle ∠AOB.

P,Qand Rare the points on the circle but on the arc ABÁåœ.

02

Step 2. Concept used:

We use compass to make a circle.

Then we make the angle

03

Step 3. Applying the concept:

At first, using a compass make a circle ⊙o.

Now, we make a central angle ∠AOB.

P,Qand Rare the points on the circle but not on ABÁåœ,

The above figure is the required figure that can be drawn from the given information.

04

Step 1. Given information:

Draw a circle ⊙oand draw a central angle ∠AOB.

P,Qand Rare the points on the circle but on the arc ABÁåœ.

05

Step 2. Concept used:

Basic concept of geometry and angles.

06

Step 3. Applying the concept:

At first, using a compass make a circle ⊙o.

Now, we make a central angle ∠AOB.

P,Qand Rare the points on the circle but not on ABÁåœ,

Now, to find the value of ∠APB,∠AQBand ∠ARB,

Use the protector placing on P,Qand Rmeasuring the values of ∠APB,∠AQBand∠ARB,

So, the values of ∠APB,∠AQBand ∠ARBare all same, that is 29°.

Therefore, the measurements of the angle are 29°,which concludes that all the angles are equal.

07

Step 1. Given information:

Draw a circle ⊙oand draw a central angle ∠AOB.

P,Qand Rare the points on the circle but on the arc ABÁåœ.

08

Step 2. Concept used:

Basic concept of geometry and angles.

09

Step 3. Applying the concept:

At first, using a compass make a circle ⊙o.

Now, we make a central angle ∠AOB.

P,QandRare the points on the circle but not on ABÁåœ,

Now, to find the value of ∠APB,∠AQBand ∠ARB,

Use the protector placing on P,Qand Rmeasuring the values of ∠APB,∠AQBand∠ARB,

So, the values of ∠APB,∠AQBand ∠ARBare all same, that is 29°.

The relation between ∠APB,∠AQBand ∠ARBis

∠APB=∠AQB=∠ARB=29∘.

Now, from the following figure, ∠AOBand ∠APBare,

So, there is no relation between∠AOBand∠APB as∠AOBis59°,which is greater than ∠APB.

Hence, the measurement of the angle are which concludes the relation∠APB=∠AQB=∠ARB=29∘,

and there is no such relation between ∠AOBand ∠APBas∠AOBis59°,which is greater than ∠APB.

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Most popular questions from this chapter

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