# Lines and Angles

#### Summary*arrow_upward*

#### Length of a line segment:

The distance between the endpoints of a line segment is the **length** of the line segment. The length of a line segment can be measured accurately using a **ruler and a divider**.

#### Complete angle:

An angle of measure **360 ^{0}** is called a complete angle.

One quadrant = ¼ (Complete angle)

= 1/4 x 360

^{0}90

^{0}=

Two quadrants = 1/2 (Complete angle) = 1/2 x 360

^{0}= 180

^{0}

Three quadrants=3/4

(Complete angle) = 3/4 x 360

^{0}= 270

^{0}

#### Right angle:

An angle that measures **90 ^{0} **is called a right angle. A right angle makes

**a quarter revolutions**.

#### Straight angle:

An angle that measures **180 ^{0}** is called a straight angle. A straight angle makes

**a half revolution**.

#### Acute angle:

An angle that measures **less than 90 ^{0}** is called an acute angle.

#### Obtuse angle:

An angle that measures **more than 90 ^{0} and less than 180^{0}** is called an obtuse angle.

#### Reflex angle:

An angle that measures **more than 180 ^{0}** is called a reflex angle.

#### Intersecting lines:

Two lines that meet each other at a single point are called intersecting lines.

#### Perpendicular lines:

Two lines that **intersect each other at right angles** are said to be perpendicular to each other.

#### Bisector of a line segment:

A bisector of a line segment is a line that divides the line segment into **two equal parts**.

#### Perpendicular bisector of a line segment:

The perpendicular line that divides a line segment into two equal parts is called the perpendicular bisector of the line segment.

#### Videos*arrow_upward*

#### Questions & Answers*arrow_upward*

### 1 . Find the angle which is equal to twice its compliment

let the angle=x

then the complemet will be=(90-x)

given,x=2(90-x)

=x=180-2x

=x+2x=180

=3x=180...

### 2 . Find the magnitude of the angles.

Sol:

1) Let the magnitude of the angle which is equal to its supplementary angle be 'x'.

? x = (180° - x)

?...

### 3 . Find the complementary and supplementary angles.

Sol:

Measure of a right angle = 90°

One third of the right angle = 30°

Complementary angle of one third of a right a...

### 4 . Find the bigger angle of the complementary angles.

Sol:

Ratio of complementary angles is 3:7

Let the angles be 3x and 7x.

3x + 7x = 90°

10x = 90°

x = 9...

### 5 . Find the supplementary angle.

Supplementary angle of 100
^{o} 30'

= 180° - 100
^{o} 30'

= 79° 30'

Or