Lines and Angles Test

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Lines and Angles Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Find the measure of the supplementary angle of $$132^o$$

A
$$48^o$$

B
$$32^o$$

C
$$42^o$$

D
$$38^o$$

Solution

Two angles are Supplementary when their sum is equal to $$180^{\circ}$$.
If one angle $$= 132^{\circ}$$, let the other angle be $$x$$.
Hence, $$ x + 132^{\circ} = 180^{\circ}$$
$$x = 180^{o} - 132^o \\= 48^o$$
Hence, supplementary angle of $$132^o$$ is $$48^o$$.
Question 2
1 / -0

OA and OB are opposite rays.
If $$x=75^o$$, what is the value of y?

A
$$105^o$$

B
$$75^o$$

C
$$45^o$$

D
$$15^o$$

Solution

Sum of $$ x $$ and $$ y $$ is equal to $$ 180^0 $$ (By Linear Pair)
A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other and supplementary means that the sum of the measures of the two angles is equal to $$180^o$$.
$$ x = 75^0 $$
$$ => x + y = 180^0 $$
$$ => 75^0 + y = 180^0 $$
$$ => y = 180^0 - 75^0 = 105^0 $$
Question 3
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Find the measure of the complementary angle of $$90^\circ$$.

A
$$0^\circ$$

B
$$45^\circ$$

C
$$90^\circ$$

D
$$60^\circ$$

Solution

The pair of angles is said to be complementary, when their sum is $$90^{o}$$.
Let $$x,y$$ be any two complementary angles and $$(\angle x)=90^{o}$$
$$\implies (\angle x)+(\angle y)=90^{o}$$ ........ (By definition of complementary angles)
$$\implies 90^{o}+(\angle y)=90^{o}$$
$$\implies (\angle y)=0^{o}$$.
Hence, measure of complementary angle of $$90^{o}$$ is $$0^{o}$$.
Hence, option $$A$$ is correct.
Question 4
1 / -0

Which angles in the given figure are complementary?

A
$$\angle\, 1$$ and $$\angle\, 2$$

B
$$\angle\, 2$$ and $$\angle\, 3$$

C
$$\angle\, 3$$ and $$\angle\, 4$$

D
$$\angle\, 4$$ and $$\angle\, 1$$

Solution

We know, two angles whose sum is equal to $$90^o$$ are known as complementary angles.
Here,
the sum, $$\angle 2+\angle 3$$, is vetrically opposite to a perpendicular.
$$\Rightarrow \angle 2+\angle 3={ 90 }^{ \circ }$$.
Hence $$\angle 2$$ and $$\angle 3$$ are complementary.
Therefore, option $$B$$ is correct.
Question 5
1 / -0

If two straight lines intersect, the measures of the vertically opposite angles are ________.

A
equal

B
not equal

C
cannot be determined

D
Nont of these

Solution

If two straight lines intersect, the measures of the vertically opposite angles are Equal.
To prove : $$\angle CBE=\angle DBA$$
We know,
$$\angle CBE+\angle DBC=180^{0}$$ ( Linear Pair)
$$=>\angle CBE=180^{0}-\angle DBC \rightarrow$$ (I)
Again,
$$\angle DBA+\angle DBC=180^{0}$$ (Linear Pair)
$$=>\angle DBA=180^{0}-\angle DBC \rightarrow $$ (II)
$$\therefore \angle CBE=\angle DBA$$.
Question 6
1 / -0

If two lines intersect such that four vertical angles are equal, then each angle is:

A
$$45^{\circ}$$

B
$$100^{\circ}$$

C
$$180^{\circ}$$

D
$$90^{\circ}$$

Solution

Let each vertical angle be $$x$$

Now the sum of vertical angles is $${ 360 }^{ \circ }$$

$$\Rightarrow x+x+x+x={ 360 }^{ \circ }\\ \Rightarrow 4x={ 360 }^{ \circ }\\ \Rightarrow x=\dfrac { { 360 }^{ \circ } }{ 4 } ={ 90 }^{ \circ }$$

So option $$D$$ is correct.
Question 7
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Supplementary angle of $$\displaystyle 102^{\circ}$$ is:

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

B
$$\displaystyle 90^{\circ}$$

C
$$\displaystyle 78^{\circ}$$

D
$$\displaystyle 60^{\circ}$$

Solution

As sum of supplementary angles if $$180^0$$
Supplementary angle of $$\displaystyle 102^{\circ}=180^{\circ}-102^{\circ}=78^{\circ}$$
Question 8
1 / -0

Given : AB || CD.
If $$\angle\, 4$$ is an obtuse angle, then $$\angle\, 5$$ is

A
Acute

B
Right

C
Obtuse

D
Straight

Solution

As $$AB||CD$$ and $$EF$$ is transversal.
$$\angle 5=\angle 4$$ (Alternate angles)
Now $$\angle 4$$ is obtuse therefore $$\angle 5$$ is also obtuse
Question 9
1 / -0

In the adjoining figure it is given that $$\displaystyle l \left | \right |m$$; t is a transversal ; then the value of x is

A
$$\displaystyle 130^{\circ}$$

B
$$\displaystyle 50^{\circ}$$

C
$$\displaystyle 120^{\circ}$$

D
None

Solution

$$\angle 1+\angle 2=180^{\circ}$$ (Adjacent angles on a straight line are supplementary)
$$\Rightarrow { 50 }^{ \circ }+\angle 2={ 180 }^{ \circ }\\ \Rightarrow \angle 2={ 180 }^{ \circ }-{ 50 }^{ \circ }\\ \Rightarrow \angle 2={ 30 }^{ \circ }$$
Now $$l||m$$ and $$t$$ is transversal
$$\therefore \angle x=\angle 2$$ (Alternate angles)
$$\Rightarrow \angle x=130^{\circ}$$
Question 10
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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.