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Lines and Angles

• Straight Line

• Angles on a straight line

• Vertically opposite angles

• Parallel lines

• Angles on a set of parallel lines

• Perpendicular lines

• Angles

• Types of Angles

• Angles at a point

• Things to know

• Calculating angles

• Straight line

The line that does not have any curves and shortest distance between two points is a straight line.

straight lines

• Angles on a straight Line

The sum of all the angles on a straight line is equal to 180°

straight line

AOB is a straight line, ∠x + ∠y + ∠z = 180°

• Vertically Opposite Angles

When two straight lines cross each other, the opposite angles formed are equal.

straight line

• Parallel lines

Parallel lines are two or more straight lines that can never meet and the distance between them is constant at all points along the lines.

angles and lines

Line AB is parallel to CD, so we write AB ∥ CD and line PQ parallel to RS so we write PQ ∥ RS.

• Angles on a set of parallel lines

When another straight line cross parallel lines it creates sets of equal angles.

straight lines

• Perpendicular lines

When two straight lines meet and form a right angle, they are known as perpendicular lines.

perpendicular line

AB is perpendicular to PQ and symbol to represent perpendicular lines is ⊥ and we write AB ⊥ PQ(AB is perpendicular to PQ)

• Angles

If two straight lines intersect at a point, then an angle is formed. The symbol of angles is ∠. The size of an angle is measured in degrees; and the symbol used to represent degree is º. The angle is shown below.

angles and lines

The intersection point of two straight lines called vertex.
Here Q is meeting point of lines PQ and QR so Q is vertex.
Lines PQ and QR are arms of the angles.
The amount of turn from one arm of the angle to the other is said to be the size of an angle.
In symbolic way we can write ∠PQR (read angle PQR).

• Types of Angles

* Right angle :-

An angle that is equal to 90°

right angle

* Acute Angle :-

An angle that is greater than 0° and less than 90° is called Acute Angle

acute angle

* Obtuse Angle :-

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

Obtuse angle

* Straight Angle :-

An angle that is exactly 180°

straight angle

* Reflex Angle :-

An angle that is greater than 180° but smaller than 360°

Reflex angle

• Angles at a point

Angles at a point or in a circle add up to 360°

In below given figure there are 4 right angles at a point

right angles at a point

angles at a point

angles at a point

• Things to know

* A square and a rectangle have 4 right angles and 4 pairs of perpendicular lines each.

square and rectangle

* A straight line has 2 right angles, which add up to 180°

straight line

* The angles in a triangle add up to 180°

• Calculating angles

calculating angle

calculating angle