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

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

A.

An isosceles triangle

B.

An acute angled triangle

C.

An obtuse angled triangle

D.

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.

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

A.

One of the angles is 35.

B.

One of the angles is 50

C.

One of the angles is 60

D.

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=95y  (i)

and, xy=25  (ii)

Substitute (i) in (ii),

95yy=25

952y=25

y=95252

y=35

So, x=9535

x=60

Third angle is 18095=85

So, the angles are 35, 60 and 85.

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

A.

37.5

B.

52.5

C.

72.5

D.

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

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

___ degrees.

#### 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=1802×40

C=100

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

A.

24 and 126

B.

42 and 156

C.

24 and 156

D.

42 and 126

#### SOLUTION

Solution : C

Since AB is a straight line, AOB=180

Therefore, AOC+COB=180

3x+30+2x60=180

5x30=180

5x=210

x=42

Therefore,

COB=2x60=8460=24

AOC=3x+30=126+30=156

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

A.

True

B.

False

#### SOLUTION

Solution : A

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

Which of the following statements is not correct?

A. An angle which is greater than 180 but less than 360 is called a reflex angle.
B. An angle greater than 0 but less than 90 is called an acute angle.
C. If the sum of two angles is 90, then they are called supplementary angles.
D. An angle greater than 90 but less than 180 is called an obtuse angle.

#### 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.

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

A.

72

B.

36

C.

100

D.

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

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

A. 60
B. 50
C. 40
D. 90

#### 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

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

A.

90+12A

B.

90+12B

C.

90+12C

D.

9012A

#### SOLUTION

Solution : A

From the given figure,
BOC = 180(2 + 4)

= 180 - (B2C2 )

= 180 - (180A2

[ 180 - A = B + C]

= 180 - 90 + A2

= 90 + A2