Lines and Angles Test

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Lines and Angles Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

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 2
1 / -0

Find x; if $$\angle\, 1\, =\, 5x\, +\, 15^{\circ}$$ and $$\angle\, 2\, =\, 28x$$, angles form linear pair.

A
$$40^{\circ}$$

B
$$140^{\circ}$$

C
$$5^{\circ}$$

D
$$20^{\circ}$$

Solution

$$\angle \, 1\, +\, \angle\, 2\, =\, 180^{\circ}$$ (Linear pair)
$$\Rightarrow\quad 5x\, +\, 15^{\circ}\, +\, 28x\, =\, 180^{\circ}$$
$$\Rightarrow\quad 33x\, =\, 180^{\circ}\, -\, 15\, =\, 165^{\circ}$$
$$\Rightarrow\quad x\, =\, \displaystyle \frac {165^{\circ}}{33}\, =\, 5^{\circ}$$.
Question 3
1 / -0

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $$3 : 7$$, then the measure of the larger angle is

A
$$54^{\circ}$$

B
$$120^{\circ}$$

C
$$126^{\circ}$$

D
$$108^{\circ}$$

Solution

Let the angles be $$3x$$ and $$7x$$.
We know that sum of two interior angles on the same side of transversal is $$180^{\circ}$$.
$$3x+7x=180 ^{\circ}$$
$$\Rightarrow 10x=180 ^{\circ}$$
$$\Rightarrow x=18 ^{\circ}$$
Therefore, the greater angle is $$7x=7\times 18=126 ^{\circ}$$
Question 4
1 / -0

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
1 / -0

Complement angle of the angle is:

A
$$77.4^{\circ}$$

B
$$67.3^{\circ}$$

C
$$76.3^{\circ}$$

D
$$77.3^{\circ}$$

Solution

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

Given, measure of one complementary angle is $$12.7^o.$$

$$\Rightarrow$$ Measure of other complementary angle $$=90^o-12.7^o$$ $$=77.3^o.$$

$$\therefore$$ Measure of a complementary angle of $$ 12.7^{o}=77.3^o$$.
Question 6
1 / -0

Two adjacent angles whose sum is $$\displaystyle 180^{0}$$ is called

A
complementary angles

B
linear pair

C
vertically opposite angles

D
none

Solution

Two adjacent angles whose sum is $$180^o$$ is called linear pair.

Ex: $$70^o+110^o = 180^o$$ then these two angles is called a linear pair.
Question 7
1 / -0

The supplementary angle of $$120^o$$ is:

A
$$30^o$$

B
$$50^o$$

C
$$240^o$$

D
$$60^o$$

Solution

Let the supplementary angle be $$x$$
Sum of supplementary angles is $$180^{\circ}$$
$$\Rightarrow x+{ 120 }^{ \circ }={ 180 }^{ \circ }\\ \Rightarrow x={ 180 }^{ \circ }-{ 120 }^{ \circ }\\ \Rightarrow x={ 60 }^{ \circ }$$
Question 8
1 / -0

Supplement angle of

A
$$122.7^{\circ}$$

B
$$131.7^{\circ}$$

C
$$132.7^{\circ}$$

D
$$132.4^{\circ}$$

Solution

Let the supplement be $$x$$
Sum of supplementary angles is $$180^{\circ}$$
$$x+47.3^{\circ}=180^{\circ}$$
$$x=180^{\circ}-47.3^{\circ}=132.7^{\circ}$$
Question 9
1 / -0

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
1 / -0

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 $$180^{\circ}$$
$$\Rightarrow x+100^{\circ}=180^{\circ}$$
$$x=180^{\circ}-100^{\circ}$$
$$x=80^{\circ}$$

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Re-Attempt Weekly Quiz Competition

Lines and Angles Test - 17

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Lines and Angles Test - 17

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SHARING IS CARING

Question 1

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

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

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

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

Solution

Question 2

$$40^{\circ}$$

$$140^{\circ}$$

$$5^{\circ}$$

$$20^{\circ}$$

Solution

Question 3

$$54^{\circ}$$

$$120^{\circ}$$

$$126^{\circ}$$

$$108^{\circ}$$

Solution

Question 4

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

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

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

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

Solution

Question 5

$$77.4^{\circ}$$

$$67.3^{\circ}$$

$$76.3^{\circ}$$

$$77.3^{\circ}$$

Solution

Question 6

complementary angles

linear pair

vertically opposite angles

none

Solution

Question 7

$$30^o$$

$$50^o$$

$$240^o$$

$$60^o$$

Solution

Question 8

$$122.7^{\circ}$$

$$131.7^{\circ}$$

$$132.7^{\circ}$$

$$132.4^{\circ}$$

Solution

Question 9

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

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

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

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

Solution

Question 10

$$180^{\circ}$$

$$90^{\circ}$$

$$80^{\circ}$$

$$60^{\circ}$$

Solution

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