Lines and Angles Test

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Lines and Angles Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

What is the value of $$x$$ in above figure?

A
$$115$$

B
$$65$$

C
$$75$$

D
$$80$$

Solution

By using the property of alternate angles, we have $$x+35=115$$
$$x=115-35$$
$$ x=80$$
Question 2
1 / -0

What is the value of $$z$$ in above figure?

A
$$58^o$$

B
$$32^o$$

C
$$132^o$$

D
$$158^o$$

Solution

According to Converse of the Alternate Interior Angles Theorem
$$\angle x=\angle z$$
And we know that $$\angle x+58^\circ=180^\circ$$
$$\Rightarrow x=132^\circ$$
$$\Rightarrow \angle z=x$$ ....Alternate angles
Therefore, $$z=132^\circ$$
Question 3
1 / -0

The supplement of an acute angle is a/an __________ angle.

A
Acute

B
Obtuse

C
Right

D
Straight

Solution

We know acute angle $$< 90^{\circ}$$
Let us take an example.
$$\angle x = 45^{\circ}$$ .....$$x$$ is an acute angle
Supplement of $$x$$ is
$$180^{\circ} - 45^{\circ} = 135^{\circ}$$ ....it is an Obtuse angle
Obtuse angle $$> 90^{\circ}$$.
Question 4
1 / -0

The measure of an angle is four times the measure of its supplementary angle. Then the angles are __________.

A
$$36^o, 144^o$$

B
$$40^o, 160^o$$

C
$$18^o, 72^o$$

D
$$50^o, 200^o$$

Solution

According to the problem,
The measure of an angle which is $$4$$ times its supplement.
Supplementary angles means, sum of angles is $$180^o$$
Let the measure of one angle be $$x$$, then the measure of its supplementary angle will be $$(180^o-x)$$.
According to the given condition,
$$\implies x=4(180^{o}-x)$$
$$\implies x=4\times 180^{o}-4x$$
$$\implies 5x=4\times 180^{o}$$
$$\implies x=4\times 36^{o}=144^{o}$$
Hence, $$x=144^{o}$$
so these angles are $$36^{\circ}$$, $$144^{\circ}$$
Hence the option $$(A)$$ is correct.
Question 5
1 / -0

The supplementary angle of an angle is one third of the angle. Then the angle and its supplement are __________.

A
$$135^o, 45^o$$

B
$$60^o, 180^o$$

C
$$120^o, 350^o$$

D
$$60^o, 120^o$$

Solution

Let the angle is $$x$$, and its supplementary angle is $$\dfrac{1}{3}x$$.
We know that the sum of the supplementary angles is $$180^o$$, then
$$x+\dfrac{1}{3}x=180^o\\ \Rightarrow \dfrac{4}{3}x=180$$
$$\Rightarrow x=\dfrac{180\times 3}{4}=135^o$$
It's supplementary angle $$=\dfrac{135}{3}=45^o$$
Question 6
1 / -0

What is the measure of supplementary angle of $$32^{\circ}$$?

A
$$58^{\circ}$$

B
$$148^{\circ}$$

C
$$138^{\circ}$$

D
$$78^{\circ}$$

Solution

Required Measure of supplementary angle $$ =180-32$$
$$ =148^0$$
Question 7
1 / -0

Find the supplement of $$98^o$$:

A
$${82^ \circ }$$

B
$${124^ \circ }$$

C
$${122^ \circ }{45^\iota }$$

D
$${135^ \circ }{20^\iota }{26^{\iota \iota }}$$

Solution

The supplement of $${98}^{\circ}$$ is the angle that when added to $${98}^{\circ}$$ forms a straight angle $${180}^{\circ}$$
To determine the supplement, subtract the given angle from $${180}^{\circ}$$.
$${180}^{\circ}-{98}^{\circ}={82}^{\circ}$$
The supplement of $${98}^{\circ}$$ is $${82}^{\circ}$$
Question 8
1 / -0

Indicate which pairs of angles are:
Vertically opposite angles.

A
1 & 4

B
2 & 4

C
1 & 3

D
5 & 4

Solution

Considering $$\angle 1=x$$ & $$\angle 5=5x$$
$$x+5x=180^o$$
$$\Rightarrow x=30^o$$
$$\angle 1=x=30^o$$
$$\angle 5=5x=150^o$$
Being vertically opposite angles,
$$\angle 5=\angle 3+\angle 2$$
$$150^o=\angle 3+\angle 2$$
$$90^o+60^o=150^o$$
$$\angle 3=90^o$$
$$\angle 2=60^o$$
$$\angle 4+\angle 3+\angle 2=180^o$$
$$\angle 4=180-(\angle 3+\angle 2)$$
$$=180-(90+60)$$
$$=30^o$$
$$\angle 1=\angle y=30^o$$
$$\therefore 1$$ & $$4$$ are vertically opposite.
Question 9
1 / -0

Find the measure of the alternate angle of the angle of measure of $${65^0}$$.

A
$${65^0}$$

B
$${25^0}$$

C
$${115^0}$$

D
Depends on the orientation of lines

Solution

Alternate angle always are equal
Hence, alternate angle of $${{65}^{0}}$$ is $${{65}^{0}}$$
Question 10
1 / -0

____ pairs of corresponding angles formed by a transversal of two parallel lines.

A
Two

B
Three

C
Four

D
Eight

Solution

We know that
$$Four$$ pairs of corresponding angles formed by a transversal of two parallel lines.

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Lines and Angles Test - 19

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Lines and Angles Test - 19

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Question 1

$$115$$

$$65$$

$$75$$

$$80$$

Solution

Question 2

$$58^o$$

$$32^o$$

$$132^o$$

$$158^o$$

Solution

Question 3

Acute

Obtuse

Right

Straight

Solution

Question 4

$$36^o, 144^o$$

$$40^o, 160^o$$

$$18^o, 72^o$$

$$50^o, 200^o$$

Solution

Question 5

$$135^o, 45^o$$

$$60^o, 180^o$$

$$120^o, 350^o$$

$$60^o, 120^o$$

Solution

Question 6

$$58^{\circ}$$

$$148^{\circ}$$

$$138^{\circ}$$

$$78^{\circ}$$

Solution

Question 7

$${82^ \circ }$$

$${124^ \circ }$$

$${122^ \circ }{45^\iota }$$

$${135^ \circ }{20^\iota }{26^{\iota \iota }}$$

Solution

Question 8

1 & 4

2 & 4

1 & 3

5 & 4

Solution

Question 9

$${65^0}$$

$${25^0}$$

$${115^0}$$

Depends on the orientation of lines

Solution

Question 10

Two

Three

Four

Eight

Solution

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