Lines and Angles Test

Result

Lines and Angles Test - 31

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Question 1
1 / -0

Supplementary angle of $$108.5^{\circ}$$ is

A
$$70.5^{\circ}$$

B
$$71.5^{\circ}$$

C
$$71^{\circ}$$

D
$$72.5^{\circ}$$

Solution

Given angle is $$= 108.5^{\circ}$$

Let the angle supplementary with the above angle be $$x$$

Now, the sum of two supplementary angles $$= 180^{\circ}$$

$$\Rightarrow x+108.5^{\circ}=180^{\circ}$$

$$\Rightarrow x=71.5^{\circ}$$
Question 2
1 / -0

Which of the following is an obtuse angle ?

A
$$92^\circ$$

B
$$181^\circ$$

C
$$195^\circ$$

D
$$83^\circ$$

Solution
Question 3
1 / -0

Choose the pair of complementary angles:

A
$$\displaystyle 66^{o} ,24^{o}$$

B
$$\displaystyle 30^{o},120^{o}$$

C
$$\displaystyle 60^{o},90^{o}$$

D
$$\displaystyle 15^{o},60^{o}$$

Solution

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

Consider option $$(A)$$.

The angles are $$66^o$$ and $$24^o$$.

Then their sum $$=66^o+24^o=90^o$$.

Hence, the angles are complementary.

Consider option $$(B)$$.

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

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

Hence, the angles are not complementary.

Consider option $$(C)$$.

The angles are $$60^o$$ and $$90^o$$.

Then their sum $$=60^o+90^o=150^o\ne90^o$$.

Hence, the angles are not complementary.

Consider option $$(D)$$.

The angles are $$15^o$$ and $$60^o$$.

Then their sum $$=15^o+60^o=75^o\ne90^o$$.

Hence, the angles are not complementary.

Hence, only option $$A$$ is correct.
Question 4
1 / -0

If two angles of a triangle are acute angles, then the third angle:

A
is less than the sum of the two angles

B
should be an acute angle

C
is the largest angle of the triangle

D
is an angle with any measurement less than $$180^o$$
Question 5
1 / -0

$$\angle AEC$$ and $$\angle CED$$ are supplementary angles. If $$\angle CED$$ is equal to $$62^{\circ}$$ ,what is the measure of $$\angle AEC$$?

A
$$28^{\circ}$$

B
$$150^{\circ}$$

C
$$118^{\circ}$$

D
$$124^{\circ}$$

Solution

Two angles are supplementary if they add up to $$180^{\circ}$$ .
As given, $$\angle AEC$$ and $$\angle CED$$ are supplementary angles,

So,
$$\angle AEC+\angle CED=180^{\circ}$$
$$\Rightarrow \angle AEC+62^{\circ}=180^{\circ}$$
$$\Rightarrow\angle AEC=180^{\circ}-62^{\circ}$$
$$\Rightarrow\angle AEC=118^{\circ}$$

Hence, the required answer is $$118^{\circ}$$.
Question 6
1 / -0

All linear pairs are

A
supplementary

B
vertically opposite

C
right angles

D
none of these

Solution

In the given diagram, $$ABC$$ is a straight line.

$$\angle ABD$$ and $$\angle CBD$$ are linear pairs.

$$\angle ABD=120^\circ$$ and $$\angle CBD=60^\circ$$

A linear pair forms a straight angle which contains $$180^\circ$$, hence the sum of $$2$$ angles measures $$180^\circ,$$ which means they are supplementary.

$$\therefore$$ $$\angle ABD+\angle CBD=120^\circ+60^\circ$$

$$=180^\circ$$

So we can say that, $$\angle ABD$$ and $$\angle CBD$$ are supplementary.

$$\therefore$$ All linear pairs are supplementary.
Question 7
1 / -0

Find the value of $$x$$ and $$y$$.

A
$$60^{\circ}, 45^{\circ}$$

B
$$45^{\circ}, 60^{\circ}$$

C
$$45^{\circ}, 45^{\circ}$$

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

Solution

From the figure, $$45^\circ$$ is the complement of $$y$$

That is, $$y + 45^\circ = 90^{\circ}$$

$$\Rightarrow$$ $$y = 90^{\circ}-45^\circ$$

$$ \Rightarrow y = 45^{\circ}$$

Also, $$30^\circ$$ is the complement of $$x$$

$$\Rightarrow x + 30^\circ = 90^\circ$$

$$\Rightarrow x = 90^\circ-30^\circ$$

$$\Rightarrow x = 60^{\circ}$$
Question 8
1 / -0

In given figure which one of the following angle is a straight angle

A
$$\angle AOB$$

B
$$\angle AOD$$

C
$$\angle BOC$$

D
$$\angle BOD$$

Solution

Straight angle is equal to $$180^o$$.
So, $$\angle BOD$$ and $$\angle AOC$$ are straight angles.
Question 9
1 / -0

The angles of a triangle are in the ratio of $$2:3:4.$$ What is the measure of the smallest interior angle of the triangle?

A
$$10^{o}$$

B
$$20^{o}$$

C
$$30^{o}$$

D
$$40^{o}$$

Solution

By angle sum property, the sum of angles is $$180^o$$.
Let $$2x, 3x$$ and $$4x$$ be the three angles.
$$2x + 3x + 4x = 180^{o}$$
$$9x = 180^{o}$$
$$x = 20^{o}$$
Smallest interior angle $$= 2 \times 20^{o} = 40^{o}.$$
Question 10
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The sum of two acute angles can be:

A
Acute angles

B
Obtuse angles

C
Right angles

D
All of the above

Solution

Let one angle is $$\displaystyle { 30 }^{ o }$$ and the other angle is $$\displaystyle { 40 }^{ o }$$ then sum is $$\displaystyle { 70 }^{ o }$$. which is an acute angle.
Let one angle is $$\displaystyle { 70 }^{ o }$$ and other angle is $$\displaystyle { 80 }^{ o }$$, then sum is $$\displaystyle { 150 }^{ o }$$ which is a obtuse angle.
Let one angle is $$\displaystyle { 45 }^{ o }$$ and another angle is $$\displaystyle { 45 }^{ o }$$ then sum is $$\displaystyle { 90 }^{ o }$$ which is a right angle.

So correct answer is $$(D)$$