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 4 of 8 pages

Question 31. In the given figure,if

\frac{y}{x} = 5 a n d \frac{z}{x} = 4

, then the value of x is

12^{\circ}

In The Given Figure,if Yx=5 and zx=4 , Then The Value Of X...

True
False
60∘
70∘

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 32. In the figure below, the value of x

^{\circ}

is:

In The Figure Below, The Value Of X∘ is:

Discuss Question

Answer: Option C. -> 30o
:
C
x + 2x + 3x = 180

^{\circ}

[Angles on a straight line]
6x = 180

^{\circ}

x = 30

^{\circ}

Question 33. In the figure given below, find

x

if AB || CD.

45∘
55∘
60∘
70∘

Discuss Question

Answer: Option B. -> 55∘
:
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 34. In the figure given below, if OP || RS, ∠OPQ = 110^o and ∠QRS = 130^o, then ∠PQR is equal to

60∘
65∘
40∘
45∘

Discuss Question

Answer: Option A. -> 60∘
:
A
Extend OP.Then, atriangle PQT will be formed;where T is the point at which OP cuts QR.

Now,

∠

OPQ +

∠

QPT = 180

^{\circ}

\Rightarrow ∠

QPT = 180

^{\circ}

-110

^{\circ}

= 70

^{\circ}

Now, since if OP || RS,

∠

SRQ and

∠

UTQ are corresponding angles hence,

∠

UTQ =

∠

SRQ = 130

^{\circ}

Therefore we have,

∠

UTQ +

∠

PTQ = 180

^{\circ}

\Rightarrow ∠

PTQ = 180

^{\circ}

- 130

^{\circ}

= 50

^{\circ}

In triangle PTQ,

∠

PTQ +

∠

TQP +

∠

QPT = 180

^{\circ}

\Rightarrow 50^{\circ}

∠

TQP +70

^{\circ}

= 180

^{\circ}

\Rightarrow ∠

TQP = 180

^{\circ}

- 120

^{\circ}

= 60

^{\circ}

\Rightarrow ∠

TQP =

∠

PQR = 60

^{\circ}

Question 35. Two parallel lines have:

A common point
Two common points
No common point
Infinite common points

Discuss Question

Answer: Option C. -> No common point
:
C

Parallel lines neverintersect. Hence, they have no common point.

Question 36. Which of the following statements is not true about the figure given below?

∠DBC = 180∘
∠CBA = 90∘
∠CBA and ∠DBA are supplementary.
∠ABD = 60∘

Discuss Question

Answer: Option D. -> ∠ABD = 60∘
:
D
Here

∠

ABD and

∠

ABC are supplementary, since they lie on a straight line.
Hence

∠

DBC = 180

^{\circ}

Given,

∠

ABC = 90

^{\circ}

∴ ∠

ABD = 180 -

∠

ABC = 180 - 90 = 90

^{\circ}

Question 37. The angle between the bisectors of two adjacent supplementary angles is a right angle.

True
False
Right angled triangle
Equilateral triangle

Discuss Question

Answer: Option A. -> True
:
A
Let

∠ A

and

∠ B

be adjacent supplementary angles as shown in the figure.

The Angle Between The Bisectors Of Two Adjacent Supplementar...

Then,

∠ A + ∠ B = 180^{\circ}

The bisectors of the angles are drawn. We have to find

∠ 1 + ∠ 2

∠ 1 + ∠ 2 = (\frac{∠ A}{2} + \frac{∠ B}{2})

= \frac{180}{2} = 90^{\circ}

Hence, the angle between the bisectors of adjacentsupplementary angles is

90^{\circ}

Question 38. If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :

Neither equal nor supplementary
Not equal but supplementary
Equal but not supplementary
Either equal or supplementary.

Discuss Question

Answer: Option D. -> Either equal or supplementary.
:
D
Let the two angles be

∠ A B C

and

∠ P Q R

.
There are two possible cases:
i)

If The Arms Of One Angle Are Respectively Parallel To The Ar...

Here,

∠ 1 = ∠ 2

[Correspoding angles] and

∠ 2 = ∠ 3

[Corresponding angles]

∴ ∠ 1 = ∠ 3

\Rightarrow ∠ A B C = ∠ P Q R

ii)

Here

∠ 1 + ∠ 2 = 180^{\circ}

[Co-interior angles] and

∠ 2 = ∠ 3

[Corresponding angles]

∴ ∠ 1 + ∠ 3 = 180^{\circ}

\Rightarrow ∠ A B C + ∠ P Q R = 180^{\circ}

Hence it can be seen that the angles could either be equal or supplementary.

Question 39. Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is

40∘
30∘
60∘
80∘

Discuss Question

Answer: Option A. -> 40∘
:
A
The sum of all the three angles of a triangle = 180

^{\circ}

Since the angles are in the ratio 2: 4 : 3, let x be a factor such that,
2x + 4x + 3x=180

^{\circ}

=> 9x = 180

^{\circ}

=> x = 20

^{\circ}

Hence the three angles of the triangle are:
=> 2x= 40

^{\circ}

=> 4x= 80

^{\circ}

=> 3x= 60

^{\circ}

So the smallest angle in the given triangle is 40

^{\circ}

Question 40. In the fig. below, if AB || CD,

∠

APQ = 50

^{\circ}

and

∠

PRD = 127

^{\circ}

, find x and y.

In The Fig. Below, If AB || CD, ∠APQ = 50∘ and ∠PRD =...

50∘, 67∘
50∘, 77∘
77∘, 87∘
77∘, 97∘

Discuss Question

Answer: Option B. -> 50∘, 77∘
:
B
Since AB || CD
∠APQ = ∠PQR (Alternate interior angles of transversal PQ)
⇒x = 50

^{\circ}

∠APR = ∠PRD (Alternate interior angles of transversal PR)
⇒y + 50

^{\circ}

= 127

^{\circ}

⇒ y = 127

^{\circ}

- 50

^{\circ}

= 77

^{\circ}

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