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 5 of 8 pages

Question 41. The angles of a triangle are in the ratio 5:3:7. The triangle is

An isosceles triangle
An acute angled triangle
An obtuse angled triangle
A right triangle

Discuss Question

Answer: Option B. -> An acute angled triangle
:
B
The sum of all the three angles of a triangle = 180

^{\circ}

Since the angles are in the ratio 5:3:7, let x be a factor such that,

5 x + 3 x + 7 x

=180

^{\circ}

\Rightarrow

15 x

=180

^{\circ}

\Rightarrow

x

=12

^{\circ}

Hence the three angles of the triangle are:

\Rightarrow

5 x

5 \times 12^{\circ}

60^{\circ}

\Rightarrow

3 x

3 \times 12^{\circ}

36^{\circ}

\Rightarrow

7 x

7 \times 12^{\circ}

84^{\circ}

Since all the angles in the triangle are less than

90^{\circ}

, the triangle is an acute angled triangle.

Question 42. In the figure, the bisector of B and C meet at O. Then

∠

BOC is

In The Figure, The Bisector Of B And C Meet At O. Then ∠ B...

90∘+12∠A
90∘+12∠B
90∘+12∠C
90∘−12∠A

Discuss Question

Answer: Option A. -> 90∘+12∠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 43. The following diagram shows parallel lines cut by a transversal. Find x.

60∘
50∘
40∘
90∘

Discuss Question

Answer: Option A. -> 60∘
:
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 44. In triangle ABC, if

B C = A C

and

∠ B = 40^{\circ}

. Then

∠ C

is equal to
___ degrees.

Discuss Question

:
In a triangle, if two sides are equal then it is an isosceles triangle. The angles opposite to the two equal sides are alsoequal.

In Triangle ABC, If BC=AC And ∠B=40∘. Then ∠C Is Equal...

Therefore,

∠ A = ∠ B

Since sum of all the angles in a triangle

= 180^{\circ}

\Rightarrow

∠ A + ∠ B + ∠ C = 180^{\circ}

\Rightarrow

2 \times 40^{\circ} + ∠ C = 180^{\circ}

(

∠ A = ∠ B

)

\Rightarrow

∠ C

= 180^{\circ} - 2 \times 40^{\circ}

\Rightarrow

∠ C

= 100^{\circ}

Question 45.

The angles of a triangle are in the ratio 5:3:7. The triangle is

An isosceles triangle
An acute angled triangle
An obtuse angled triangle
A right triangle

Discuss Question

Answer: Option B. -> An acute angled triangle
:
B

The sum of all the three angles of a triangle = 180 $^{\circ}$

Since the angles are in the ratio 5:3:7, let x be a factor such that,

$5 x + 3 x + 7 x$ =180 $^{\circ}$

$\Rightarrow$ $15 x$ =180 $^{\circ}$

$\Rightarrow$ $x$ =12 $^{\circ}$

Hence the three angles of the triangle are:

$\Rightarrow$ $5 x$ = $5 \times 12^{\circ}$ = $60^{\circ}$

$\Rightarrow$ $3 x$ = $3 \times 12^{\circ}$ = $36^{\circ}$

$\Rightarrow$ $7 x$ = $7 \times 12^{\circ}$ = $84^{\circ}$

Since all the angles in the triangle are less than $90^{\circ}$ , the triangle is an acute angled triangle.

Question 46.

The sum of the two angles in a triangle is $95^{\circ}$ and their difference is $25^{\circ}$ . Then which of the following are true?

One of the angles is $35^{\circ}$ .
One of the angles is $50^{\circ}$
One of the angles is $60^{\circ}$
One of the angles is $85^{\circ}$

Discuss Question

Answer: Option B. -> One of the angles is

50^{\circ}

:
A, C, and D

Let the two angles be $x$ and $y$ .

So, $x + y = 95^{\circ}$
$\Rightarrow x = 95^{\circ} - y$ $\cdot \cdot \cdot$ (i)

and, $x - y = 25^{\circ}$ $\cdot \cdot \cdot$ (ii)
Substitute (i) in (ii),
$\Rightarrow 95^{\circ} - y - y = 25^{\circ}$

$\Rightarrow 95^{\circ} - 2 y = 25^{\circ}$
$\Rightarrow y = \frac{95^{\circ} - 25^{\circ}}{2}$
$\Rightarrow y = 35^{\circ}$

So, $x = 95^{\circ} - 35^{\circ}$

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

Third angle is $180^{\circ} - 95^{\circ} = 85^{\circ}$

So, the angles are $35^{\circ}$ , $60^{\circ}$ and $85^{\circ}$ .

Question 47.

An exterior angle of a triangle is 105^o and its two interior opposite angles are equal. Each of these equal interior angles are

37.5 $^{\circ}$
52.5 $^{\circ}$
72.5 $^{\circ}$
75 $^{\circ}$

Discuss Question

Answer: Option B. -> 52.5

^{\circ}

:
B

From the properties of triangles:

Exterior angle = Sum of interior opposite angles

Now let us take each interior opposite angle as x ( as both interior opposite angles are equal)

⇒ x + x = 105 $^{\circ}$

⇒ 2x = 105 $^{\circ}$

⇒ x = 52.5 $^{\circ}$

So the value of each of the opposite interior angle = 52.5 $^{\circ}$

Question 48.

From the figure given below, find out the measure of $∠$ COB and $∠$ AOC respectively.

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

Discuss Question

Answer: Option C. -> 24

^{\circ}

and 156

^{\circ}

:
C

Since AB is a straight line, $∠ A O B = 180^{\circ}$

Therefore, $∠ A O C + ∠ C O B = 180^{\circ}$

$\Rightarrow 3 x + 30^{\circ} + 2 x - 60^{\circ} = 180^{\circ}$

$\Rightarrow 5 x - 30^{\circ} = 180^{\circ}$

$\Rightarrow 5 x = 210^{\circ}$

$\Rightarrow x = 42^{\circ}$

Therefore,

$∠ C O B = 2 x - 60^{\circ} = 84^{\circ} - 60^{\circ} = 24^{\circ}$

$∠ A O C = 3 x + 30^{\circ} = 126^{\circ} + 30^{\circ} = 156^{\circ}$

Question 49.

In triangle ABC, if $B C = A C$ and $∠ B = 40^{\circ}$ . Then $∠ C$ is equal to

___ degrees.

Discuss Question

Answer: Option C. -> 24

^{\circ}

and 156

^{\circ}

In a triangle, if two sides are equal then it is an isosceles triangle. The angles opposite to the two equal sides are also equal.

Therefore, $∠ A = ∠ B$

Since sum of all the angles in a triangle $= 180^{\circ}$

$\Rightarrow$ $∠ A + ∠ B + ∠ C = 180^{\circ}$

$\Rightarrow$ $2 \times 40^{\circ} + ∠ C = 180^{\circ}$ ( $∠ A = ∠ B$ )

$\Rightarrow$ $∠ C$ $= 180^{\circ} - 2 \times 40^{\circ}$

$\Rightarrow$ $∠ C$ $= 100^{\circ}$

Question 50.

Which of the following statements is not correct?

An angle which is greater than $180^{\circ}$ but less than $360^{\circ}$ is called a reflex angle.
An angle greater than $0^{\circ}$ but less than $90^{\circ}$ is called an acute angle.
If the sum of two angles is $90^{\circ}$ , then they are called supplementary angles.
An angle greater than $90^{\circ}$ but less than $180^{\circ}$ is called an obtuse angle.