Lines and Angles Test

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Lines and Angles Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the greater of the two angles is

A
54°

B
108°

C
120°

D
136°

Solution

Let the angles be 2x and 3x

Therefore

2x + 3x = 180°( sum of co interior angles is 180°)

5x = 180°

x = \(\frac{180}{5}\)

x = 36°

Therefore larger angle = 3 x 36° = 108°
Question 2
1 / -0

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

A
an isosceles triangle

B
an obtuse triangle

C
an equilateral triangle

D
a right triangle

Solution

Let the angles of a AABC be ∠A, ∠B and ∠C.

Given, ∠A = ∠B+∠C …(i)

In MBC, ∠A+ ∠B+ ∠C = 180° [sum of all angles of atriangle is 180°]…(ii)

From Eqs. (i) and (ii),

∠A +∠A = 180°

2∠A = 180°

∠A = 90°

Hence, the triangle is a right triangle.
Question 3
1 / -0

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

A
\(37 \frac{1}{2}^o\)

B
\(52 \frac{1}{2}^o\)

C
\(72 \frac{1}{2}^o\)

D
\(75^o\)

Solution

Let one of interior angle be x°.

Sum of two opposite interior angles = Exterior angle

x° + x° = 105°

2x° = 105°

x° = \(\frac{105}{2}^o\)

x°= \(52 \frac{1}{2}^o\)

Hence, each angle of a triangle is \(52 \frac{1}{2}^o\).
Question 4
1 / -0

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

A
an acute angled triangle

B
an obtuse angled triangle

C
a right triangle

D
an isosceles triangle

Solution

Given, the ratio of angles of a triangle is 5 : 3 : 7.

Let angles of a triangle be ∠A,∠B and ∠C.

Then, ∠A = 5x, ∠B = 3x and ∠C = 7x

In ΔABC, ∠A + ∠B + ∠C = 180° [since, sum of all angles of a triangle is 180°]

5x + 3x + 7x = 180°

15x = 180°

x = 180°/15= 12°

∠A = 5x = 5 x 12° = 60°

∠B = 3x = 3 x 12°= 36°

and ∠C = 7x = 7 x 12° = 84°

Since, all angles are less than 90°, hence the triangle is an acute angled triangle.
Question 5
1 / -0

If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be

A
50°

B
65°

C
145°

D
155°

Solution

Let three angles of the triangle are ∠A, ∠B, and ∠C

Let ∠C = 130°

Then ∠A + ∠B = 180° - 130° = 50° [since ∠A + ∠B + ∠C = 180° ]

Now, ∠C + ∠A/2 + ∠B/2 = 180° [∠A/2 and ∠B/2 are the bisector and in a triangle sum of all angles is 180° ]

∠C + ∠(A + B)/2 = 180°

∠C + 50°/2 = 180°

∠C + 25° = 180°

∠C = 180° - 25°

∠C = 155°
Question 6
1 / -0

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

A
60°

B
40°

C
80°

D
20°

Solution

Given, the ratio of angles of a triangle is 2 : 4 : 3.

Let the angles of a triangle be ∠A, ∠B and ∠C.

∠A = 2x, ∠B = 4x

∠C = 3x ,

∠A +∠B + ∠C = 180° [sum of all the angles of a triangle is 180°]

2x + 4x + 3x = 180°

9x = 180°

x=180°/9 = 20°

∠A = 2x = 2 x 20° = 40°

∠B = 4x = 4 x 20° = 80°

∠C = 3x = 3 x 20° = 60°

Hence, the smallest angle of a triangle is 40°.
Question 7
1 / -0

If an angle differs from its complement by 10, the angle is

A
\(60^o\)

B
\(40^o\)

C
\(50^o\)

D
\(80^o\)

Solution

let angles is x then its complement is 90 - x° .

Now given x° - (90 - x° ) = 10

x° - 90° + x° = 10

2x° = 10 + 90 = 100

x° = \(100°\over 2\) = 50°

∴ Required angle is 50° .
Question 8
1 / -0

If two lines intersected by a transversal, then each pair of corresponding angles so formed is

A
Equal

B
Complementary

C
Supplementary

D
None of these
Question 9
1 / -0

Two parallel lines have :

A
a common point

B
two common point

C
no any common point

D
infinite common points

Solution

Two parallel lines have no any common point.
Question 10
1 / -0

The angle between the bisectors of two adjacent supplementary angles is:

A
acute angle

B
right angle

C
obtuse angle

D
none of these

Solution

The angle between the bisectors of two adjacent supplementary angles is right angle.
Question 11
1 / -0

An angle is \(14^o\) more than its complementary angle then angle is :

A
\(38^o\)

B
\(52^o\)

C
\(50^o\)

D
none of these

Solution

Given that,

An angle is 14° more than its complementary angle

The angle measured is ‘x’ say

The complementary angle of ‘x’ is (90-x)°

It is given that

x - (90° - x) = 14°

x - 90° + x = 14°

2x = 90° + 14°

2x = 104°

x = \(104^o \over2\)

x = 52°
Question 12
1 / -0

If the supplement of an angle is three times its complement, then angle is:

A
\(30^o\)

B
\(40^o\)

C
\(50^o\)

D
\(45^o\)

Solution

Given that,

Supplementary of an angle = 3 times its complementary angle.

The angles measured will be x°

Supplementary angle of x will be 180° - x° and

The complementary angle of x will be (90 - x)°

It’s given that

Supplementary of angle = 3 times its complementary angle

180° - x° = 3(90° - x°)

180° - x° = 270° - 3x°

3x° - x° = 270° - 180°

2x° = 90°

x = 45°

Angled measured is 45°.
Question 13
1 / -0

Which one of the following statements is not false:

A
if two angles forming a linear pair, then each of these angles is of measure \(90^o\)

B
angles forming a linear pair can both be acute angles

C
one of the angles forming a linear pair can be obtuse angle

D
bisectors of the adjacent angles form a right angle

Solution

One of the angles forming a linear pair can be obtuse angle is not false.
Question 14
1 / -0

If the angles (2x −10)° and (x − 5)° are complementary angles, the value of x is

A
\(35^o\)

B
\(40^o\)

C
\(45^o\)

D
\(50^o\)

Solution

Given that,

(2x - 10)° and (x - 5)° are complementary angles.

Let x be the measured angle.

Since the angles are complementary

Their sum will be 90°

(2x -10) + (x - 5) = 90°

3x - 15° = 90°

3x = 90° + 15°

x = 105°

x = \(105^0 \over3\) = 35°

x = 35°
Question 15
1 / -0

How many pairs of adjacent angles are formed when two lines intersect in a point?

A
3

B
4

C
5

D
6

Solution

Four pairs of adjacent angle formed when two lines intersect in a point they are

∠AOD, ∠DOB

∠DOB, ∠BOC

∠COA, ∠AOD

∠BOC, ∠COA

Hence 4 pairs.
Question 16
1 / -0

If one angle of a linear pair is acute, then its other angle will be _____

A
Acute angle

B
Right angle

C
Supplement angle

D
Obtuse angle

Solution

If one angle of a linear pair is acute, then its other angle will be Obtuse angle.
Question 17
1 / -0

A ray stands on a line, then the sum of the two adjacent angles so formed is ______

A
\(90^o\)

B
\(100^o\)

C
\(180^o\)

D
\(360^o\)

Solution

A ray stands on a line, then the sum of the two adjacent angles so formed is 180°.
Question 18
1 / -0

If the sum of two adjacent angles is 180°, then the ______ arms of the two angles are opposite rays.

A
Common

B
Uncommon

C
Equal

D
Unequal

Solution

If the sum of two adjacent angles is 180°, then the uncommon arms of the two angles are opposite rays.

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Lines and Angles Test - 17

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Lines and Angles Test - 17

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Question 1

54°

108°

120°

136°

Solution

Question 2

an isosceles triangle

an obtuse triangle

an equilateral triangle

a right triangle

Solution

Question 3

\(37 \frac{1}{2}^o\)

\(52 \frac{1}{2}^o\)

\(72 \frac{1}{2}^o\)

\(75^o\)

Solution

Question 4

an acute angled triangle

an obtuse angled triangle

a right triangle

an isosceles triangle

Solution

Question 5

50°

65°

145°

155°

Solution

Question 6

60°

40°

80°

20°

Solution

Question 7

\(60^o\)

\(40^o\)

\(50^o\)

\(80^o\)

Solution

Question 8

Equal

Complementary

Supplementary

None of these

Question 9

a common point

two common point

no any common point

infinite common points

Solution

Question 10

acute angle

right angle

obtuse angle

none of these

Solution

Question 11

\(38^o\)

\(52^o\)

\(50^o\)

none of these

Solution

Question 12

\(30^o\)

\(40^o\)

\(50^o\)

\(45^o\)

Solution

Question 13