# Free Lines and Angles 03 Practice Test - 7th grade

### Question 1

Which of the following can be classified as the smaller angle between the hour hand and minute hand at 8 o'clock?

Acute Angle

Right Angle

Obtuse Angle

Straight Angle

#### SOLUTION

Solution :C

A clock has a total of 360°.

The angle between any two consecutive numbers on a clock

= 360∘12 = 30∘ [∵ a clock has 12 divisions]At 8 o'clock, the minute hand is at 12 and the hour hand is at 8 and there are 4 divisions between 8 and 12.

∴ The angle between them = 4 × 30∘

= 120∘

Hence the angle formed at 8 o'clock is an obtuse angle since it is more than 90° and less than 180°.

### Question 2

Find the measure of ∠2, ∠3 and ∠4 from the given figure.

75∘, 75∘, 105∘

75∘, 85∘, 105∘

105∘, 75∘, 75∘

105∘, 75∘, 105∘

#### SOLUTION

Solution :D

From the figure given in the question, we can observe that

∠3 = 75∘

(Vertically opposite angles)

∠2 +75∘ = 180∘

(Angles on a straight line)

⇒ ∠2 = 180∘- 75∘ = 105∘

∠2 = ∠4

(Vertically opposite angles)

⇒∠4 = 105°

### Question 3

In the figure given below, identify the exterior angles.

1, 2, 7, 8.

1, 2, 5, 7.

3, 2, 5, 6.

3, 4, 8, 7.

#### SOLUTION

Solution :A

Exterior angles lie outside the parallel lines. The exterior angles are 1, 2, 7, 8.

### Question 4

In figure given below, Find the value of ∠1 + ∠2.

#### SOLUTION

Solution :C

∠1 and 72∘ form a linear pair.

So, ∠1 + 72∘ = 180°

⇒ ∠1 = 180°- 72∘

⇒ ∠1 = 108°

Similarly, ∠2 and 98∘ form a linear pair.

So, ∠2 + 98∘ = 180°

⇒ ∠2 = 180°- 98∘

⇒ ∠2 = 82°

∴∠1+∠2=108°+82°=190°

### Question 5

Find the angle between the hour hand and minute hand when the clock shows 2 p.m.

Ans:

#### SOLUTION

Solution :A circular clock consists of 360 degrees. The angle between any two consecutive numbers of a clock is.

36012 = 30∘.

At 2 PM, the minute hand is at 12 and the hour hand is at 2.

Therefore the angle between them = 2 × 30 = 60∘

### Question 6

An angle of measure 30∘ and twice of another angle x are supplementary angles. Find the value of x (in degrees).

Ans:

#### SOLUTION

Solution :Two angles are called supplementary angles if their sum is 180∘.

So, 30∘ + 2x = 180∘

Hence, x = 75∘.

### Question 7

If three lines are cut by two transversals, then there are

#### SOLUTION

Solution :If three lines are cut by two transversals, then there are 6 points of intersection.

### Question 8

All angles greater than 90∘ are obtuse angles. True or false.

True

False

#### SOLUTION

Solution :B

Angles less than 90∘ are acute angles.

An obtuse angle is more than 90° but less than 180°

Angles equal to 90∘ are right angles.

### Question 9

"Only one transversal can be drawn for any two given lines". True/False?

True

False

#### SOLUTION

Solution :B

Infinite number of transversals can be drawn for any two given lines.

### Question 10

Parallel lines intersect at infinity.

True

False

#### SOLUTION

Solution :B

Parallel lines never intersect.