Shapes and Angles Test 4

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Shapes and Angles Test 4

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Question 1
1 / -0

If one angle at a point is reflex angle, the other at that point may be :

A
Acute angle

B
Obtuse angle

C
Straight angle

D
Acute or obtuse angle

Solution

We know, the angle formed at a point is $$\displaystyle { 360 }^{ o }$$.
When one of angle is reflex, it range from $$\displaystyle { 180 }^{ o }$$ to $$\displaystyle { 360 }^{ o }$$.
If angle is $$\displaystyle { 200 }^{ o }$$ then the other angle is $$\displaystyle { 160 }^{ o }$$, i.e obtuse angle.
If one reflex angle is $$\displaystyle { 300 }^{ o }$$ then other angle is $$\displaystyle { 60 }^{ o }$$ i.e acute angle.
Hence, the option $$D$$ is correct.
Question 2
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Reflex angle is greater than _____ but less than _____angle.

A
Complete, acute

B
Acute, Straight

C
Obtuse, Straight

D
Straight, Complete

Solution

Reflex angle is the angle which is greater than $$\displaystyle {180}^{ o }$$ and less than $$\displaystyle {360 }^{ o }$$.
Straight angle is $$\displaystyle { 180 }^{ o }$$ and complete angle is $$\displaystyle { 360 }^{ o }$$.

So reflex angle is greater than straight angle and less than complete angle.
Question 3
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What is the range of reflex angle?

A
Greater than zero but less than $$\displaystyle { 90 }^{ o }$$

B
Greater than $$\displaystyle { 90 }^{ o }$$ but less than $$\displaystyle { 180 }^{ o }$$

C
Greater than $$\displaystyle { 180 }^{ o }$$ but less than $$\displaystyle { 360 }^{ o }$$

D
Equal to $$\displaystyle { 360 }^{ o }$$

Solution

Acute angle is the angle which is greater than $$\displaystyle { 0 }^{ o }$$ and less than $$\displaystyle { 90 }^{ o }$$.
Obtuse angle is the angle which is greater than $$\displaystyle { 90}^{ o }$$ and less than $$\displaystyle {180 }^{ o }$$.
Right angle is the angle which is equal to $$90^o$$.

Now, by definition, reflex angle is the angle which is greater than $$\displaystyle {180}^{ o }$$ and less than $$\displaystyle {360 }^{ o }$$.
That is, angles larger than a straight angle but less than $$1$$ turn (between $$180^o$$ and $$360^o$$) are called reflex angles.

Therefore, the range of reflex angle is greater than $$180^o$$ but less than $$360^o$$.
Hence, option $$C$$ is correct.
Question 4
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Which of the following is a reflex angle?

A
$$\displaystyle { 180 }^{ o }$$

B
$$\displaystyle { 360 }^{ o }$$

C
$$\displaystyle { 204 }^{ o }$$

D
$$\displaystyle { 135 }^{ o }$$

Solution

We know, reflex angle must be between $$\displaystyle { 180 }^{ o }$$ and $$\displaystyle { 360 }^{ o }$$. It can't be equal to $$\displaystyle { 180 }^{ o }$$ or $$\displaystyle { 360 }^{ o }$$ as these are straight and complete angle, respectively.

Here, only $$204^o$$ is greater than $$180^o$$ and less than $$360^o$$.
Therefore, option $$C$$ is correct.
Question 5
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Which of the following is a straight angle?

A
Angle that is less that $$90^{\circ}$$

B
Angle that is exactly $$90^{\circ}$$

C
Angle that is greater than $$90^{\circ}$$

D
None of these

Solution

Straight angle is the angle which is exactly $$180^{\circ}$$

Hence option $$D$$ is the correct answer.
Question 6
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Sum of two obtuse angle results in:

A
Acute angle

B
Right angle

C
Obtuse angle

D
Reflex angle

Solution

Obtuse angle ranges from $$\displaystyle { 90 }^{ o }$$ to $$\displaystyle { 180 }^{ o }$$
So, sum of least obtuse angle is $$\displaystyle { 91 }^{ o }+{ 91 }^{ o }={ 182 }^{ o }$$, which is a reflex angle.
Now, sum of maximum obtuse angle is $$\displaystyle { 179 }^{ o }+{ 179 }^{ o }={ 358 }^{ o }$$, which is also a reflex angle.

Acute angle is the angle which is greater than $$\displaystyle { 0 }^{ o }$$ and less than $$\displaystyle { 90 }^{ o }$$.
Obtuse angle is the angle which is greater than $$\displaystyle { 90}^{ o }$$ and less than $$\displaystyle {180 }^{ o }$$.
Right angle is the angle which is equal to $$90^o$$.
Reflex angle is the angle which is greater than $$\displaystyle {180}^{ o }$$ and less than $$\displaystyle {360 }^{ o }$$.
Question 7
1 / -0

Let's divide a circle into $$10$$ equal parts. Then, the measure of each central angle of a circle is :

A
$$18^{o}$$

B
$$72^{o}$$

C
$$36^{o}$$

D
$$30^{o}$$

Solution

Since, circle divides in 10 equal parts, total measure angle at centre $$=360°$$.
So, each central angle after division is $$=\cfrac{360°}{10}=36°$$
Question 8
1 / -0

At which one of the following times is the angle between the hands of a clock exactly one right angle?

A
$$3$$:$$30$$

B
$$3$$:$$00$$

C
$$12$$:$$00$$

D
None of these

Solution

Angle between the hands of clock is exactly right angle at $$3$$:$$00$$
So option $$B$$ is correct.
Question 9
1 / -0

How many right angles are there in $$540^o$$?

A
$$4$$

B
$$6$$

C
$$8$$

D
none of these

Solution

One right angle $$=90^{\circ}$$
Let there be $$x$$ right angles in $$540^{\circ}$$
$$\Rightarrow { 90 }^{ \circ }x={ 540 }^{ \circ }\\ \Rightarrow x=\dfrac { { 540 }^{ \circ } }{ { 90 }^{ \circ } } =6$$
So option $$B$$ is correct.
Question 10
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The central angle of each part is:

A
$$60^\circ$$

B
$$30^\circ$$

C
$$45^\circ$$

D
$$90^\circ$$

Solution

You can clearly see the circle is divided into $$12$$ equal parts.
Total Central angle $$=360^{\circ}$$
Let measure of central angle $$=x$$
$$\\ \Rightarrow 12(x)={ 360 }^{ \circ }\\ \Rightarrow 12x={ 360 }^{ \circ }\\ \Rightarrow x=\dfrac { { 360 }^{ \circ } }{ 12 } \\ \Rightarrow x={ 30 }^{ \circ }$$
So option $$B$$ is correct.