Lines and Angles Test

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Lines and Angles Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Reflex angle is greater than _____ but less than _____angle.

A
Complete, acute

B
Acute, Straight

C
Obtuse, Straight

D
Straight, Complete

Solution

Reflex angle is the angle which is greater than $$\displaystyle {180}^{ o }$$ and less than $$\displaystyle {360 }^{ o }$$.
Straight angle is $$\displaystyle { 180 }^{ o }$$ and complete angle is $$\displaystyle { 360 }^{ o }$$.

So reflex angle is greater than straight angle and less than complete angle.
Question 2
1 / -0

If one acute angle of the right angled triangle is half of the other, then the smallest angle is:

A
$$\displaystyle { 90 }^{ o }$$

B
$$\displaystyle { 60 }^{ o }$$

C
$$\displaystyle { 40 }^{ o }$$

D
$$\displaystyle { 30 }^{ o }$$

Solution

Let the acute angle be $$x$$.
Given, the acute angle is half of the other.
Then the other angle is $$2x$$.

We know, by angle sum property, the sum of angles of a triangle is $$\displaystyle { 180 }^{ o }$$.
$$\implies$$ $$\displaystyle { 90 }^{ o }+2x+x={ 180 }^{ o }$$
$$\implies$$ $$\displaystyle 3x={ 180 }^{ o }-{ 90 }^{ o }$$
$$\implies$$$$\displaystyle x=\frac { { 90 }^{ o } }{ 3 } $$
$$\implies$$$$\displaystyle x={ 30 }^{ o }$$.

Hence, the angles are:
$$90^o, x=30^o$$ and $$2x=2\times30^o=60^o$$.

Here, $$30^o$$ is the smallest angle.

Therefore, option $$D$$ is correct.
Question 3
1 / -0

Which of the following is a straight angle?

A
Angle that is less that $$90^{\circ}$$

B
Angle that is exactly $$90^{\circ}$$

C
Angle that is greater than $$90^{\circ}$$

D
None of these

Solution

Straight angle is the angle which is exactly $$180^{\circ}$$

Hence option $$D$$ is the correct answer.
Question 4
1 / -0

Two angles the sum of whose measure is $$90^{\circ}$$ are called ______ angles.

A
Supplementary

B
Complementary

C
Corresponding

D
None of these

Solution

By definition we know that two angles, the sum of whose measure is $$ { 90^o } $$ are called complementary angles.
Then, such angles are called complement of each other.

E.g.: Let the measure of one complementary angle is $$58^o.$$

$$\Rightarrow$$ Measure of other complementary angle $$=90^o-58^o$$ $$=32^o.$$

$$\therefore$$ Measure of the complementary angle of $$ 58^{o}=32^o$$.
Hence, $$ 58^{o}$$ and $$32^o$$ are complements of each other.

Therefore, option $$B$$ is correct.
Question 5
1 / -0

If two angles are supplementary, then their sum is

A
$$90^o$$

B
$$180^o$$

C
$$270^o$$

D
$$360^o$$

Solution

If two angles are supplementary , then their sum is $${ 180 ^o } $$
Question 6
1 / -0

Find the supplement of the angle
$$148^{\circ}$$

A
$$32^{\circ}$$

B
$$122^{\circ}$$

C
$$148^{\circ}$$

D
None of these

Solution

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

So,
The supplement angle of $$148^0$$ will be
$$=180^0-148^0=32^0$$

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

Corresponding angle converse theorem states that :

A
If two lines and transversal form corresponding angles that are congruent , then the lines are parallel

B
If two lines and transversal form alternate interior angles that are congruent , then the lines are parallel

C
If two parallel lines are cut by Transversal then the pair of corresponding angles are congruent

D
If two lines intersect each other,then the vertically opposite angles are equal

Solution

Corresponding angle converse theorem states that, If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
Question 8
1 / -0

The converse of alternate angle theorem states that :

A
If two parallel lines are cut by Transversal then the pair of corresponding angles are congruent

B
If two parallel lines are cut by transversal, then the pair of alternate interior angles are equal

C
If two lines and a transversal form corresponding angles that are congruent,then the lines are parallel

D
If two lines intersect each other,then the vertically opposite angles are equal

Solution

The converse of alternate angle theorem states that, If two lines and a transversal form alternate corresponding angles that are congruent, then the lines are parallel.
Question 9
1 / -0

In a triangle, the angles are in ratio $$1: 3: 2$$. Find the difference between the greatest and smallest angle of the triangle.

A
$$10^o$$

B
$$70^o$$

C
$$60^o$$

D
$$20^o$$

Solution

Given, the angles are in the ratio $$1:3:2$$.

Let the angles be $$x,3x$$ and $$2x$$.

Using angle sum property of triangle,
$$x+3x+2x={ 180 }^{ \circ }\\ \Rightarrow 6x={ 180 }^{ \circ }\\ \Rightarrow x={ 30 }^{ \circ }.$$

So the angles are :
$$x={ 30 }^{ \circ }$$,
$$ 3x=3\times { 30 }^{ \circ }={ 90 }^{ \circ }$$
and $$2x=2\times { 30 }^{ \circ }={ 60 }^{ \circ }$$.

Therefore, the difference between the greatest and the smallest angle $$={ 90 }^{ \circ }-{ 30 }^{ \circ }={ 60 }^{ \circ }$$.

Hence, option $$C$$ is correct.
Question 10
1 / -0

Which type of angle best describes angle Q?

A
Obtuse

B
Acute

C
Right

D
Straight

Solution

Measure of angle $$Q$$ is more thaan $$90^o$$ but less than $$180^o$$.
Hence the $$\angle Q$$ is an obtuse angle.