Shapes and Angles Test 9

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Shapes and Angles Test 9

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Weekly Quiz Competition

Question 1
1 / -0

Look at the angle in the picture and choose the correct option

A
Right angle

B
Less than Right angle

C
More than Right angle

D
None of these

Solution
Question 2
1 / -0

Mark the correct alternative of the following.
The number of degrees in $$3$$ right angles is?

A
$$180^o$$

B
$$360^o$$

C
$$270^o$$

D
$$90^o$$

Solution

As we know $$1$$ right angle$$=90^o$$.
So $$3$$ right angles $$=3\times 90^o=270^o$$.
Question 3
1 / -0

Mark the correct alternative of the following.
An angle of measure $$140^o$$ is?

A
An acute angle

B
An obtuse angle

C
A straight angle

D
A complete angle

Solution

An angle that measures $$<180^o$$ but $$>90^o$$ is called an obtuse angle.
Here it is given $$140^o$$, so it is an obtuse angle.
Question 4
1 / -0

Mark the correct alternative of the following.
The number of degrees in $$2$$ right angles is?

A
$$90^o$$

B
$$180^o$$

C
$$270^o$$

D
$$360^o$$

Solution

$$2$$ right angles $$=2\times 90^o=180^o$$.
Question 5
1 / -0

Measures of the two angles between an hour and minute hands of a clock at 9'O clock are

A
$${ 60 }^{ o },{ 300 }^{ o }$$

B
$${ 270 }^{ o },{ 90 }^{ o }$$

C
$${ 75 }^{ o },{ 285 }^{ o }$$

D
$${ 30 }^{ o },{ 300 }^{ o }$$

Solution

We know that $$60\ minute={360}^{o}$$
So, $$1\ minute =6^{\circ}$$
Number of minutes between $$9'O$$ clock and $$12'O$$ clock is $$15$$ in clockwise direction and $$45$$ in anticlockwise direction
$$\therefore$$ Required angle $$=45\times { 6 }^{ o }={ 270 }^{ o }$$ in anticlockwise direction;
And $$15\times { 6 }^{ o }={ 90 }^{ o }$$ in clockwise direction
Hence, option $$B$$ is correct.
Question 6
1 / -0

An angle measuring $$270^{o}$$ is:

A
an obtuse angle

B
an acute angle

C
a straight angle

D
a reflex angle

Solution

The given measure of angle is $$270^o.$$
Reflex angles are angles measuring greater than $$180^o$$ and less than $$360^o.$$
$$\therefore$$ $$270^o$$ is a reflex angle.
Hence, option $$D$$ is correct.
Question 7
1 / -0

If bicycle wheel has $$48$$spokes, then the angle between a pair of two consecutive spokes are

A
$$\left( 5\cfrac { 1 }{ 2 } \right) $$

B
$$\left( 3\cfrac { 3 }{ 4 } \right) $$

C
$$\left( \cfrac { 2 }{ 11 } \right) $$

D
$$\left( \cfrac { 2 }{ 15 } \right) $$

Solution

A bicycle wheel is circular in shape and circle forms $$360^o$$ angle at the center.
$$1$$ spoke divides angle in two parts.
A bicycle wheel has $$48$$ spokes, then the angle formed on circle is divided into $$2\times 48=96$$ parts

So, the angle between a pair of two consecutive is $$=\cfrac { 360 }{ 96 } =\cfrac{90}{24}=\cfrac{15}{4}=\cfrac{12+3}{4}=\left(3\cfrac { 3 }{ 4}\right)^0$$
Hence, option $$B$$ iis correct.
Question 8
1 / -0

In figure, if point $$A$$ is shifted to point $$B$$ along the ray $$PX$$ such that $$PB=2PA$$, then the measure of $$\angle BPY$$ is

A
Greater than $${ 45 }^{ o }$$

B
$${ 45 }^{ o }$$

C
Less than $${ 45 }^{ o }$$

D
$${ 90 }^{ o }$$

Solution

Increments and decrement in the length of arms of an angle does not affect measure of angle.
So, if $$A$$ is shifted then still arm will remain same, so angle will also remain same.
$$\therefore \angle BPY={ 45 }^{ o }\quad $$
Hence, option $$B$$ is correct
Question 9
1 / -0

In figure, lines $$PQ$$ and $$ST$$ intersect at $$O$$. If $$\angle POR=90^o$$ and $$x:y =3:2$$, then $$z$$ is equal to

A
$$126^o$$

B
$$144^o$$

C
$$136^o$$

D
$$154^o$$

Solution

We can see in the given figure, $$PQ$$ is a straight line
$$\therefore \angle POR +ROT +\angle TOQ =180^o$$
$$\Rightarrow 90^o +x+y=180^o$$
$$\Rightarrow x+y=90^o$$
$$\Rightarrow x+y=90^o$$ ...(1)
Given that, $$\dfrac xy =\dfrac 32$$
Let $$x=3K$$ and $$y=2K$$
From equation (1)
$$\Rightarrow 3K+2K=90^o$$
$$\Rightarrow K=\dfrac{90^o}{5}$$
$$\Rightarrow K=18^o$$
$$\therefore y=2\times 18^o =36^o$$
Now, $$SOT$$ is a straight line
$$\Rightarrow z+y=180^o$$
$$\Rightarrow z+36^o =180^o$$
$$\Rightarrow z=180^o-36^o$$
$$\Rightarrow z=144^o$$
Hence, Option $$(B)$$ is correct.
Question 10
1 / -0

In figure, the value of $$x$$ is

A
$$110^o$$

B
$$46^o$$

C
$$64^o$$

D
$$150^o$$

Solution

Option (d) is correct.
As we knew, the angle made around a point is $$360$$ degree.
Then,
$$\therefore y+64^o +46^o +100^o -360^o$$
$$\Rightarrow y+210^o =360^o $$
$$\Rightarrow y=360^o -210^o$$
$$\Rightarrow y=150^o$$

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Re-Attempt Weekly Quiz Competition

Shapes and Angles Test 9

Result

Shapes and Angles Test 9

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SHARING IS CARING

Question 1

Right angle

Less than Right angle

More than Right angle

None of these

Solution

Question 2

$$180^o$$

$$360^o$$

$$270^o$$

$$90^o$$

Solution

Question 3

An acute angle

An obtuse angle

A straight angle

A complete angle

Solution

Question 4

$$90^o$$

$$180^o$$

$$270^o$$

$$360^o$$

Solution

Question 5

$${ 60 }^{ o },{ 300 }^{ o }$$

$${ 270 }^{ o },{ 90 }^{ o }$$

$${ 75 }^{ o },{ 285 }^{ o }$$

$${ 30 }^{ o },{ 300 }^{ o }$$

Solution

Question 6

an obtuse angle

an acute angle

a straight angle

a reflex angle

Solution

Question 7

$$\left( 5\cfrac { 1 }{ 2 } \right) $$

$$\left( 3\cfrac { 3 }{ 4 } \right) $$

$$\left( \cfrac { 2 }{ 11 } \right) $$

$$\left( \cfrac { 2 }{ 15 } \right) $$

Solution

Question 8

Greater than $${ 45 }^{ o }$$

$${ 45 }^{ o }$$

Less than $${ 45 }^{ o }$$

$${ 90 }^{ o }$$

Solution

Question 9

$$126^o$$

$$144^o$$

$$136^o$$

$$154^o$$

Solution

Question 10

$$110^o$$

$$46^o$$

$$64^o$$

$$150^o$$

Solution

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