# Free Lines and Angles 03 Practice Test - 9th Grade

### Question 1

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

#### SOLUTION

Solution :B

The sum of all the three angles of a triangle = 180∘

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

5x+3x+7x =180∘

⇒ 15x =180∘

⇒ x =12∘

Hence the three angles of the triangle are:

⇒ 5x =5×12∘ =60∘

⇒ 3x =3×12∘ =36∘

⇒ 7x =7×12∘ =84∘

Since all the angles in the triangle are less than 90∘, the triangle is an acute angled triangle.

### Question 2

The sum of the two angles in a triangle is 95∘ and their difference is 25∘. Then which of the following are true?

One of the angles is 35∘.

One of the angles is 50∘

One of the angles is 60∘

One of the angles is 85∘

#### SOLUTION

Solution :A, C, and D

Let the two angles be x and y.

So, x+y=95∘

⇒x=95∘−y ⋅⋅⋅ (i)and, x−y=25∘ ⋅⋅⋅ (ii)

Substitute (i) in (ii),

⇒95∘−y−y=25∘⇒95∘−2y=25∘

⇒y=95∘−25∘2

⇒y=35∘So, x=95∘−35∘

⇒ x=60∘

Third angle is 180∘−95∘=85∘

So, the angles are 35∘, 60∘ and 85∘.

### Question 3

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∘

52.5∘

72.5∘

75∘

#### SOLUTION

Solution :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∘

⇒ 2x = 105∘

⇒ x = 52.5∘

So the value of each of the opposite interior angle = 52.5∘

### Question 4

In triangle ABC, if BC=AC and ∠B=40∘. Then ∠C is equal to

#### SOLUTION

Solution :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∘

⇒ ∠A+∠B+∠C=180∘

⇒ 2×40∘+∠C=180∘

^{ }(∠A=∠B)⇒ ∠C=180∘−2×40∘

⇒ ∠C=100∘

### Question 5

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

24∘ and 126∘

42∘ and 156∘

24∘ and 156∘

42∘ and 126∘

#### SOLUTION

Solution :C

Since AB is a straight line, ∠AOB=180∘

Therefore, ∠AOC+∠COB=180∘

⇒3x+30∘+2x−60∘=180∘

⇒5x−30∘=180∘

⇒5x=210∘

⇒x=42∘

Therefore,

∠COB=2x−60∘=84∘−60∘=24∘

∠AOC=3x+30∘=126∘+30∘=156∘

### Question 6

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

True

False

#### SOLUTION

Solution :A

The sum of two complementary angles is 90∘. Hence, each angle will be less than 90∘

### Question 7

Which of the following statements is not correct?

#### SOLUTION

Solution :C

a)An acute angle measures between 0∘ and 90∘, whereas a right angle is exactly equal to 90∘.

b)An angle greater than 90∘ but less than 180∘ is called an obtuse angle.

c)An angle which is greater than 180∘ but less than 360∘ is called a reflex angle.

d)If the sum of two angles is 90∘,^{ }then they are called complementary angles and if the sum is 180∘, then they are called supplementary angles.

### Question 8

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

72∘

36∘

100∘

144∘

#### SOLUTION

Solution :A

Let ∠1 = 3x and ∠2 = 2x

Sum of angles on a straight line is 180∘.

So, 3x + 2x = 180∘

⇒ 5x = 180∘

⇒ x = 36∘

⇒∠6 = ∠2 [∵∠6 and ∠2 are corresponding angles]

⇒ ∠6 = 2x = 2 × 36 = 72∘Hence, ∠6 = 72∘

### Question 9

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

#### SOLUTION

Solution :A

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

⇒ 2x - 60∘

^{ }= x⇒ x - 60∘ = 0

⇒ x = 60∘

### Question 10

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

90∘+12∠A

90∘+12∠B

90∘+12∠C

90∘−12∠A

#### SOLUTION

Solution :A

From the given figure,

∠BOC = 180∘−(∠2 + ∠4)= 180∘

^{ }- (∠B2 + ∠C2 )= 180∘

^{ }- (180∘−∠A2)^{ }[∵ 180∘ - ∠ A = ∠ B + ∠ C]= 180∘

^{ }- 90∘ + ∠A2= 90∘

^{ }+ ∠A2