Lines and Angles Test

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Lines and Angles Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

In the figure above, $$\displaystyle \overline { AB } \parallel \overline { CD } ,\overline { AE } $$ bisects $$\displaystyle \angle BAC$$ and $$\displaystyle \overline { CE } $$ bisects $$\displaystyle \angle ACD$$. Find the measure of $$\displaystyle \angle AEC$$ if the measure of $$\displaystyle \angle BAC$$ is $$\displaystyle { 82 }^{ \circ }$$.

A
$$\displaystyle { 86 }^{ \circ }$$

B
$$\displaystyle { 88 }^{ \circ }$$

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

D
$$\displaystyle { 92 }^{ \circ }$$

E
Cannot be determined from the given information

Solution

Given, $$\angle A=82^{0}$$
Hence, $$\angle C=180^{0}-82^{0}=98^{0}$$...(angles on the same side of the tansversal).
Therefore, $$\angle EAC=\dfrac{\angle A}{2}=41^{0}$$
Similarly $$\angle ECA=\dfrac{\angle C}{2}=49^{0}$$
Therefore, $$\angle CEA=180^{0}-(\angle EAC+\angle ECA)=180^{0}-(90)=90^{0}$$.
Question 2
1 / -0

Find the complement of each of the following angles $$24^{\circ}$$.

A
$$66^{\circ}$$

B
$$156^{\circ}$$

C
$$36^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$24^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-24^o$$ $$=66^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 24^{o}=66^o$$.
Therefore, option $$A$$ is correct.
Question 3
1 / -0

Find the complement of each of the following angles $$48^{\circ}$$.

A
$$42^{\circ}$$

B
$$52^{\circ}$$

C
$$132^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$

Given, measure of one complementary angle is $$48^o.$$

$$\Rightarrow$$ Measure of other complementary angle $$=90^o-48^o$$ $$=42^o.$$

$$\therefore$$ Measure of a complementary angle of $$ 48^{o}=42^o$$.
Therefore, option $$A$$ is correct.
Question 4
1 / -0

Find the complement of each of the following angles $$35^{\circ}$$.

A
$$55^{\circ}$$

B
$$145^{\circ}$$

C
$$35^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$35^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-35^o$$ $$=55^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 35^{o}=55^o$$.
Therefore, option $$A$$ is correct.
Question 5
1 / -0

Find the complement of the following angles:
$$63^{\circ}$$.

A
$$27^{\circ}$$

B
$$54^{\circ}$$

C
$$117^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when their sum is equal to $$90^o.$$
Given, measure of one angle is $$63^o.$$
$$\Rightarrow$$ Measure of its complementary angle $$=90^o-63^o$$ $$=27^o.$$
$$\therefore$$ Measure of complementary angle of $$ 63^{o}=27^o$$.
Option $$A$$ is correct.
Question 6
1 / -0

Find the supplement of the following angle.
$$40^{\circ}$$

A
$$140$$

B
$$40$$

C
$$10$$

D
None of these

Solution

We know that the supplement angle
$$=180^0-\theta$$

So,
The supplement angle of $$40^0$$ will be
$$=180^0-40^0=140^0$$

Hence, this is the answer.
Question 7
1 / -0

Find the complement of each of the following angles $$20^{\circ}$$.

A
$$70^{\circ}$$

B
$$60^{\circ}$$

C
$$110^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$20^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-20^o$$ $$=70^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 20^{o}=70^o$$.
Therefore, option $$A$$ is correct.
Question 8
1 / -0

Two angles are equal and supplementary to each other. find them.

A
$$ 90^0 , \, 90^0$$

B
$$ 30^0 , \, 150^0$$

C
$$ 45^0 , \, 45^0$$

D
None of these
Question 9
1 / -0

What is the value of $$a+b$$?

A
$$120$$

B
$$180$$

C
$$60$$

D
None of these

Solution

From diagram, we can say
$$a=180^\circ-120^\circ=60^\circ$$
and $$b=180^\circ-60^\circ=120^\circ$$
Therefore, $$ a+b=60+120=180^\circ$$
Question 10
1 / -0

What is the measure of supplementary angle of $$108^{\circ}$$?

A
$$76^{\circ}$$

B
$$62^{\circ}$$

C
$$72^{\circ}$$

D
$$82^{\circ}$$

Solution

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Re-Attempt Weekly Quiz Competition

Lines and Angles Test - 25

Result

Lines and Angles Test - 25

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Rank

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SHARING IS CARING

Question 1

$$\displaystyle { 86 }^{ \circ }$$

$$\displaystyle { 88 }^{ \circ }$$

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

$$\displaystyle { 92 }^{ \circ }$$

Cannot be determined from the given information

Solution

Question 2

$$66^{\circ}$$

$$156^{\circ}$$

$$36^{\circ}$$

None of these

Solution

Question 3

$$42^{\circ}$$

$$52^{\circ}$$

$$132^{\circ}$$

None of these

Solution

Question 4

$$55^{\circ}$$

$$145^{\circ}$$

$$35^{\circ}$$

None of these

Solution

Question 5

$$27^{\circ}$$

$$54^{\circ}$$

$$117^{\circ}$$

None of these

Solution

Question 6

$$140$$

$$40$$

$$10$$

None of these

Solution

Question 7

$$70^{\circ}$$

$$60^{\circ}$$

$$110^{\circ}$$

None of these

Solution

Question 8

$$ 90^0 , \, 90^0$$

$$ 30^0 , \, 150^0$$

$$ 45^0 , \, 45^0$$

None of these

Question 9

$$120$$

$$180$$

$$60$$

None of these

Solution

Question 10

$$76^{\circ}$$

$$62^{\circ}$$

$$72^{\circ}$$

$$82^{\circ}$$

Solution

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