# Math Assignment Help With Angles

## 9.2 Angles:

When a ray OA starting from its original position, rotates about its fixed point O, to a final position OB, then an angle AOB is formed. Point O is called the Vertex of the angle.

**9.2.1 Measure of the angle: **It is defined as the amount of rotation from initial side to final side.

**9.2.1.1 Degree measure (Sexagesimal System):** The number of degrees on the circumference of circle between initial and final sides of the angle is called its degree measure. Each degree is divided into 60 equal parts called minutes and each minute is divided into another 60 equal parts named as seconds.

Degree is denoted by the symbol (** ^{o}**), minute is denoted by the symbol (

**‘**) and second is denoted by the symbol (

**“**).

**Example:** 35^{o} 34’ 23’’ means 35 degrees 34 minutes and 23 seconds.

Types of angles: For an angle θ

Acute angle:- 0^{o} ≤ θ <90^{o}

Obtuse angle: 90^{o} < θ <180^{o}

Reflex angle: 180^{o} < θ <360^{o}

Right angle: θ = 90^{o}

Straight angle: θ = 180^{o}

**9.2.1.2 Radian measure:** It is the measure of an angle subtended at the centre of a circle of radius **r** by an arc of the length **r.** To convert from degrees to radians, multiply by (π/180^{o}). To convert from radians

to degrees, multiply by (180^{o}/π).

9.2.1.3 Grade measure: Each right angle is divided into 100 equal parts known as grades. Each grade is subdivided into 100 equal parts called as minutes. Each minute is subdivided into 100 equal parts known as seconds.

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