Angle

**Category : **5th Class

Inclination between two rays having common end point is called angle.

In the above given picture, OA and OB are two rays which have a common end point 0. Point 0 is called vertex and rays OA and OB are called arms. The inclination between the rays OA and OB is called angle AOB, and it is denoted as \[\angle \text{AOB}\text{.}\]

Angle is measured in degree. Symbol of the degree is \[~{{''}^{o}}''\] and written as \[{{a}^{o}}.\]

**Types of Angle**

There are different types of angles.

(a) Acute angle

(b) Right Angle

(c) Obtuse angle

(d) Straight angle

**Acute Angle**

An angle which measures between 0° and 90° is called acute angle.

**Measure the given below angle and find is it an acute angle. **

**Explanation**

Measure of the above given angle is \[{{40}^{o}}.\]

Therefore, the angle is an acute angle

**Right Angle**

An angle of \[{{90}^{o}}\] is called right angle.

**Obtuse Angle**

An angle which measures between \[{{90}^{o}}\] and \[{{180}^{o}}\] is called obtuse angle.

**Straight Angle**

An angle which measures \[{{180}^{o}}\] is called straight angle.

**Triangle **

The geometrical shapes having three sides are called triangle.

**Properties of Triangle**

Triangle has:

(i) Three sides,

(ii) Three angles

(iii) Three vertices

Three sides of the triangle \[\text{XYZ}\]are\[\text{ }\!\!~\!\!\text{ XY, YZ,}\] and \[\text{ZX}\]

Three angles of the triangle are \[\angle \text{X,}\angle \text{Y,}\]and \[\angle Z\]

Three vertices of the triangle are point \[\text{X,}\] point Y, and point Z.

**Types of Triangle**

Triangle has been classified:

(a) On the basis of sides

(b) On the basis of angles

**Sides Based Classification**

On the basis of sides, triangles are of three types

(i) Equilateral Triangle

(ii) Isosceles Triangle

(iii) Scalene Triangle

** Equilateral Triangle**

A triangle whose all sides are of equal length is called equilateral triangle.

\[\Delta \] ABC is an equilateral triangle as AB = BC = AC = 4 cm.

**Note:** All the angles of an equilateral triangles are of \[{{60}^{o}}\]

**Isosceles Triangle**

A triangle whose any two sides are of equal length is called isosceles triangle.

\[\Delta \] ABC is an isosceles triangle as AB = AC 5 cm.

**Note:** In an isosceles triangle, opposite angles of equal sides are equal

**Scalene Triangle**

A triangle whose all sides are of different length is called scalene triangle.

\[\Delta \] PQR is a scalene triangle as \[PQ\ne QR\ne PR.\]

**Note:** In a scalene triangle, no angles are equal

**Angle Based Classification**

On the basis of angles, triangle are of three types

(i) Acute-angled Triangle

(ii) Right-angled Triangle

(iii) Obtuse-angled Triangle

**Acute-Angled Triangle**

A triangle having all angles between 90° and 0° is called acute-angled triangle.

ABC is an acute-angled triangle as its each angle (\[\angle A,\angle B,\angle C\]) measures between \[{{0}^{o}}\] and \[{{90}^{o}}.\]

**Right-Angled Triangle **

A triangle having an angle of 90° is called a right-angled triangle.

\[\Delta \]ABC is a right-angled triangle as it contains a right angle(\[\Delta ABC\])

**Obtuse-Angled Triangle**

A triangle having one obtuse angle is called obtuse-angled triangle.

\[\Delta \]MNP is an obtuse-angled triangle as it contains an obtuse angle (\[\angle MNP\])

*play_arrow*Introduction*play_arrow*Point and Line Segment*play_arrow*Angle*play_arrow*Quadrilateral*play_arrow*Geometrical Figures*play_arrow*Geometrical Figures

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