Lines and Angles Test

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Lines and Angles Test - 21

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Question 1
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Based on the given figure, which of the following statements is true?

A
$$\angle\, 5$$ and $$\angle\, 7$$ are supplementary angles.

B
$$\angle\, 7\, =\, 55^\circ$$

C
$$\angle\, 8$$ and $$\angle\, 1$$ are corresponding angles.

D
$$\angle\, 4$$ and $$\angle\, 5$$ are alternate angles.

Solution

$$\angle 5$$ and $$\angle 7$$ are vertically opposite angles.
$$\angle 6=55^{\circ}$$ (Alternate angles)
$$\angle 7+\angle 6=180^{\circ}$$ (Adjacent angle on straight line)
$$\Rightarrow \angle 7+{ 55 }^{ \circ }={ 180 }^{ \circ }\\ \Rightarrow \angle 7={ 125 }^{ \circ }$$
$$\angle 1$$ and $$\angle 8$$ are not corresponding angles.
$$\angle 4$$ and $$\angle 5$$ are alternate angles.
So only option $$D$$ is correct.
Question 2
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Two complementary angles are in the ratio $$1:9$$. The angles are:

A
$$54^\circ,\, 36^\circ$$

B
$$9^\circ,\, 81^\circ$$

C
$$10^\circ,\, 90^\circ$$

D
$$11^\circ,\, 79^\circ$$

Solution

Given, the complementary angles are in the ratio $$1:9$$.
Let the angles be $$x$$ and $$9x$$.
We know, sum of the complementary angles is $$90^{ \circ }$$.
$$\Rightarrow x+9x={ 90 }^{ \circ }\\ \Rightarrow 10x=9{ 0 }^{ \circ }\\ \Rightarrow x=9^{ \circ }$$

Hence, the angles are:
$$x=1\times 9^{ \circ }=9^{ \circ }$$
and $$ 9x=9\times 9^{ \circ }=81^{ \circ }$$.

Therefore, option $$B$$ is correct.
Question 3
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$$\displaystyle 179^{\circ}$$ is an example of

A
obtuse angle.

B
acute angle.

C
right angle.

D
None of the above

Solution

An obtuse angle is an angle which is more than $$90^o $$ but less than $$180^o$$.
Hence $$\displaystyle 179^{\circ}$$ is an example of obtuse.

Hence $$Op-A$$ is correct.
Question 4
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Which two angles are supplementary?

A
$$\angle\, COF$$ and $$\angle\, AOC$$

B
$$\angle\, COF$$ and $$\angle\, COE$$

C
$$\angle\, COF$$ and $$\angle\, EOD$$

D
$$\angle\, COF$$ and $$\angle\, AOE$$

Solution

$$\angle COF$$ and $$\angle COE$$ are supplementary because they formed on the line $$EOF$$
$$\Rightarrow \angle COF+\angle COE={ 180 }^{ \circ }$$
So option $$B$$ is correct.
Question 5
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$$\displaystyle 89^{\circ}$$ is an example of :

A
obtuse

B
acute

C
right

D
None of the above

Solution

Angles between $$ {0}^{o} $$ and $$ {90}^{o} $$ are acute angles. Hence, $$ {89}^{o} $$ is an acute angle.
Question 6
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If two angles in a triangle are $$40^o$$ and $$60^o$$, then the third angle is:

A
$$90^o$$

B
$$80^o$$

C
$$70^o$$

D
$$60^o$$

Solution

Let the third angle be $$x$$
We know, by angle sum property, the sum of all angles of a triangles is $$ 180^0$$.
$${ 40 }^{ \circ }+{ 60 }^{ \circ }+x={ 180 }^{ \circ }\\ { 100 }^{ \circ }+x={ 180 }^{ \circ }\\ \Rightarrow x={ 80 }^{ \circ }$$
Question 7
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An angle which measures $$180^{\circ}$$ is called_______angle.

A
zero

B
right

C
straight

D
acute

Solution

An angle which measures $$ {180}^{o} $$ is called a straight angle.
Question 8
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An angle which measures more than $$\displaystyle 0^{\circ}$$ and less than $$\displaystyle 90^{\circ}$$ is called

A
obtuse

B
acute

C
right

D
none of these

Solution

Angles which measure more than $$ {0}^{o} $$ and less than $$ {90}^{o} $$ are acute angles.
Question 9
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Choose the pair of complementary angles:

A
$$30^{\circ}$$, $$150^{\circ}$$

B
$$76^{\circ}$$, $$14^{\circ}$$

C
$$65^{\circ}$$, $$65^{\circ}$$

D
$$120^{\circ}$$, $$30^{\circ}$$

Solution

We know, two angles whose sum is equal to $$90^o$$ are known as complementary angles.

Consider option $$(A)$$.

The angles are $$30^o$$ and $$150^o$$.

Then their sum $$=30^o+150^o=180^o\ne90^o$$.

Hence, the angles are not complementary.

Consider option $$(B)$$.

The angles are $$76^o$$ and $$14^o$$.

Then their sum $$=76^o+14^o=90^o$$.

Hence, the angles are complementary.

Consider option $$(C)$$.

The angles are $$65^o$$ and $$65^o$$.

Then their sum $$=65^o+65^o=130^o\ne90^o$$.

Hence, the angles are not complementary.

Consider option $$(D)$$.

The angles are $$120^o$$ and $$30^o$$.

Then their sum $$=120^o+30^o=150^o\ne90^o$$.

Hence, the angles are not complementary.

Hence, only option $$B$$ is correct.
Question 10
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Supplementary angle of $$100^{\circ}$$ is

A
$$180^{\circ}$$

B
$$90^{\circ}$$

C
$$80^{\circ}$$

D
$$60^{\circ}$$

Solution

Let the supplement be $$x$$
If angles are supplementary then their sum is $$180^{\circ}$$
$$\Rightarrow x+100^{\circ}=180^{\circ}$$
$$x=180^{\circ}-100^{\circ}$$
$$x=80^{\circ}$$