Lines and Angles Test

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Lines and Angles Test - 20

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Question 1
1 / -0

$$\displaystyle \angle AOB$$ is a / an _____________ angle.

A
acute

B
right

C
obtuse

D
none of these

Solution

An obtuse angle is one which measures more than $$90^o$$ but less than $$180^o$$.
Question 2
1 / -0

Find the measure of the supplementary angle of $$132^o$$

A
$$48^o$$

B
$$32^o$$

C
$$42^o$$

D
$$38^o$$

Solution

Two angles are Supplementary when their sum is equal to $$180^{\circ}$$.
If one angle $$= 132^{\circ}$$, let the other angle be $$x$$.
Hence, $$ x + 132^{\circ} = 180^{\circ}$$
$$x = 180^{o} - 132^o \\= 48^o$$
Hence, supplementary angle of $$132^o$$ is $$48^o$$.
Question 3
1 / -0

OA and OB are opposite rays.
If $$x=75^o$$, what is the value of y?

A
$$105^o$$

B
$$75^o$$

C
$$45^o$$

D
$$15^o$$

Solution

Sum of $$ x $$ and $$ y $$ is equal to $$ 180^0 $$ (By Linear Pair)
A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other and supplementary means that the sum of the measures of the two angles is equal to $$180^o$$.
$$ x = 75^0 $$
$$ => x + y = 180^0 $$
$$ => 75^0 + y = 180^0 $$
$$ => y = 180^0 - 75^0 = 105^0 $$
Question 4
1 / -0

Fill in the blanks with the correct word from the options given.
Parallel lines are ____ intersecting lines.

A
Always

B
Never

C
Sometimes

D
Data Insuficient

Solution

Parallel lines are never intersecting lines.
Option $$B$$ is correct.
Question 5
1 / -0

Which angles in the given figure are complementary?

A
$$\angle\, 1$$ and $$\angle\, 2$$

B
$$\angle\, 2$$ and $$\angle\, 3$$

C
$$\angle\, 3$$ and $$\angle\, 4$$

D
$$\angle\, 4$$ and $$\angle\, 1$$

Solution

We know, two angles whose sum is equal to $$90^o$$ are known as complementary angles.
Here,
the sum, $$\angle 2+\angle 3$$, is vetrically opposite to a perpendicular.
$$\Rightarrow \angle 2+\angle 3={ 90 }^{ \circ }$$.
Hence $$\angle 2$$ and $$\angle 3$$ are complementary.
Therefore, option $$B$$ is correct.
Question 6
1 / -0

Given : AB || CD.

If $$\angle\, 2$$ is an acute angle, then $$\angle\, 1$$ is

A
Acute

B
Right

C
Obtuse

D
Straight

Solution

$$\angle 1$$ and $$\angle 2$$ are supplementary angles .
$$\Rightarrow \angle 1+\angle 2={ 180 }^{ \circ }$$
Now $$\angle 2$$ is given acute
$$\Rightarrow \angle 2<{ 90 }^{ \circ }$$
$$\Rightarrow \angle 1>{ 90 }^{ \circ }$$
So it is an obtuse angle.
Question 7
1 / -0

Straight angle is ________

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

B
$$\displaystyle 180^{\circ}$$

C
$$\displaystyle 60^{\circ}$$

D
$$\displaystyle 45^{\circ}$$

Solution

A straight angle $$ = {180}^{o} $$
Question 8
1 / -0

Supplementary angle of $$\displaystyle 102^{\circ}$$ is:

A
$$\displaystyle 180^{\circ}$$

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

C
$$\displaystyle 78^{\circ}$$

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

Solution

As sum of supplementary angles if $$180^0$$
Supplementary angle of $$\displaystyle 102^{\circ}=180^{\circ}-102^{\circ}=78^{\circ}$$
Question 9
1 / -0

Based on the angle measures given, which triangle is not acute?

A
$$35^\circ,\, 69^\circ,\, 76^\circ$$

B
$$60^\circ,\, 60^\circ,\, 60^\circ$$

C
$$88^\circ,\, 46^\circ,\, 46^\circ$$

D
$$90^\circ,\, 45^\circ,\, 45^\circ$$

Solution

For acute angles triangle all the three angles must be less than $${ 90 }^{ \circ }$$.
In option $$D$$ one of the angle is $${ 90 }^{ \circ }$$ , so it is not acute angles triangle.
Question 10
1 / -0

$$\displaystyle 91^{\circ}$$ is an example of

A
obtuse

B
acute

C
right

D
Reflex

Solution

An obtuse angle is one which is more than $$90^0$$ but less than $$180^0$$.
and hence $$\displaystyle 91^{\circ}$$ is an example of obtuse.