Lines And Angles(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

LINES AND ANGLES MCQs

Lines And Angles

Total Questions : 74 | Page 6 of 8 pages

Question 51.

If two angles are complementary to each other, then each angle is an acute angle.

True
False
24 $^{\circ}$ and 156 $^{\circ}$
42 $^{\circ}$ and 126 $^{\circ}$

Discuss Question

Answer: Option A. -> True
:
A

The sum of two complementary angles is 90 $^{\circ}$ . Hence, each angle will be less than 90 $^{\circ}$

Question 52.

The following diagram shows parallel lines cut by a transversal. Find x.

60 $^{\circ}$
50 $^{\circ}$
40 $^{\circ}$
90 $^{\circ}$

Discuss Question

Answer: Option A. -> 60

^{\circ}

:
A

In the above figure, since the two lines are parallel and cut by a transversal, using the property of corresponding angles:

$\Rightarrow$ 2x - 60 $^{\circ}$ = x

$\Rightarrow$ x - 60 $^{\circ}$ = 0

$\Rightarrow$ x = 60 $^{\circ}$

Question 53.

In the figure, the bisector of B and C meet at O. Then $∠$ BOC is

$90^{\circ} + \frac{1}{2} ∠ A$
$90^{\circ} + \frac{1}{2} ∠ B$
$90^{\circ} + \frac{1}{2} ∠ C$
$90^{\circ} - \frac{1}{2} ∠ A$

Discuss Question

Answer: Option A. ->

90^{\circ} + \frac{1}{2} ∠ A

:
A

From the given figure,
$∠$ BOC = 180 $^{\circ} - (∠$ 2 + $∠$ 4)

= 180 $^{\circ}$ - ( $\frac{∠ B}{2}$ + $\frac{∠ C}{2}$ )

= 180 $^{\circ}$ - ( $\frac{180^{\circ} - ∠ A}{2}$ ) [ $∵$ 180 $^{\circ}$ - $∠$ A = $∠$ B + $∠$ C]

= 180 $^{\circ}$ - 90 $^{\circ}$ + $\frac{∠ A}{2}$

= 90 $^{\circ}$ + $\frac{∠ A}{2}$

Question 54.

In the adjoining figure AB || CD, ∠1 : ∠2 = 3 : 2. Then ∠6 is _____

72 $^{\circ}$
36 $^{\circ}$
100 $^{\circ}$
144 $^{\circ}$

Discuss Question

Answer: Option A. -> 72

^{\circ}

:
A

Let $∠$ 1 = 3x and $∠$ 2 = 2x

Sum of angles on a straight line is 180 $^{\circ}$ .

So, 3x + 2x = 180 $^{\circ}$

⇒ 5x = 180 $^{\circ}$

⇒ x = 36 $^{\circ}$

⇒ $∠$ 6 = $∠$ 2 [ $∵$ ∠6 and ∠2 are corresponding angles]
⇒ $∠$ 6 = 2x = 2 × 36 = 72 $^{\circ}$

Hence, $∠$ 6 = 72 $^{\circ}$

Question 55.

In the adjoining figure, the value of $∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F$ in degrees is

___

Discuss Question

Answer: Option A. -> 72

^{\circ}

From $△$ ABC;

$∠ A + ∠ B + ∠ C = 180^{\circ}$

From $△$ DEF;

$∠ D + ∠ E + ∠ F = 180^{\circ}$

So, adding these

$∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F = 1 80^{\circ} + 180^{\circ} = 360^{\circ}$

Question 56.

In the figure given below, find $x$ if AB || CD.

45 $^{\circ}$
55 $^{\circ}$
60 $^{\circ}$
70 $^{\circ}$

Discuss Question

Answer: Option B. -> 55

^{\circ}

:
B

From the given figure,

$∠ E C D = 180^{\circ} - 150^{\circ} = 30^{\circ}$ (sum of interior angles on the same side of the transversal is 180°)

$x = ∠ B C D = 25^{\circ} + ∠ E C D$ (alternate interior angles)
$= 25^{\circ} + 30^{\circ} = 55^{\circ}$

Question 57.

The sides BC, CA and AB of $Δ A B C$ are produced in order to form exterior angles $∠ A C D$ , $∠ B A F$ and $∠ C B E$ respectively, then $∠ B A F + ∠ A C D + ∠ C B E$ is

$180^{\circ}$
$270^{\circ}$
$360^{\circ}$
$540^{\circ}$

Discuss Question

Answer: Option C. ->

360^{\circ}

:
C

By angle sum property,
$x + y + z = 180^{\circ}$
$∠ B A F + ∠ A C D + ∠ C B E$
$= (180^{\circ} - x) + (180^{\circ} - y) + (180^{\circ} - z)$
$= 540^{\circ} - (x + y + z) = 540^{\circ} - 180^{\circ} = 360^{\circ}$

Question 58.

In the given figure,if $\frac{y}{x} = 5 a n d \frac{z}{x} = 4$ , then the value of x is $12^{\circ}$ .

True
False
60 $^{\circ}$
70 $^{\circ}$

Discuss Question

Answer: Option B. -> False
:
B

$\frac{y}{x} = 5$
$\Rightarrow y = 5 x$ and
$\frac{z}{x} = 4$
$\Rightarrow z = 4 x$
$x^{\circ} + y^{\circ} + z^{\circ} = 180^{\circ}$
$x^{\circ} + 5 x^{\circ} + 4 x^{\circ} = 180^{\circ}$
$10 x^{\circ} = 180^{\circ}$
$x = 18^{\circ}$

Question 59.

Which one of the following statements are true?

If two angles form a linear pair, then each of these angles is of measure $180^{\circ}$ .
Angles forming a linear pair can both be acute angles.
One of the angles forming a linear pair can be obtuse angle.
The sum of the angles of a linear pair is $180^{\circ}$ .

Discuss Question

Answer: Option C. -> One of the angles forming a linear pair can be obtuse angle.
:
C and D

If two angles form a linear pair, either both of them are $90^{\circ}$ or one angle is acute and the other is obtuse. They cannot both be acute angles because in that case the sum would not be $180^{\circ}$ .