We know that

Angle subtended at center of circle = 360°

And we studied that

Angle subtended at center of circle = 2π radians

So,

360° = 2π radians

360°/2 = π radians

180° = π radians

To convert degrees and radians,

Radian measure = π/180 × Degree measure

Let’s look at some examples

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Convert 30° into radians
**

Radian measure = π/180 × Degree measure

Radian measure = π/180 × 30

Radian measure = π × 30/180

Radian measure = π × 1/6

Radian measure = π/6

∴ 30° = π/6 radians

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**
Convert
**
**
45°
**
**
into radians
**

Radian measure = π/180 × Degree measure

Radian measure = π/180 × 45

Radian measure = π × 45/180

Radian measure = π × 1/4

Radian measure = π/4

∴ 45° = π/4 radians

####
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Convert 60° into radians
**

Radian measure = π/180 × Degree measure

Radian measure = π/180 × 60

Radian measure = π × 60/180

Radian measure = π × 1/3

Radian measure = π/3

∴ 60° = π/3 radians

####
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Convert
**
**
90°
**
**
into radians
**

Radian measure = π/180 × Degree measure

Radian measure = π/180 × 90

Radian measure = π × 90/180

Radian measure = π × 1/2

Radian measure = π/2

∴ 90° = π/2 radians

####
**
Convert 0° into radians
**

Radian measure = π/180 × Degree measure

Radian measure = π/180 × 0

Radian measure = 0

∴ 30° = 0 radians

####
**
Convert
**
**
π
**
**
radians into degree
**

Radian measure = π/180 × Degree measure

π = π/180 × Degree measure

π × 180/π = Degree measure

180 = Degree measure

Degree measure = 180

∴ π radian = 180°

####
**
Convert
**
**
π
**
**
/6 radians into degree
**

Radian measure = π/180 × Degree measure

π/6 = π/180 × Degree measure

π/6 × 180/π = Degree measure

π/π × 180/6 = Degree measure

1 × 30 = Degree measure

30 = Degree measure

Degree measure = 30

∴ π/6 radian = 30°

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Convert
**
**
π
**
**
/3
**
**
radians into degree
**

Radian measure = π/180 × Degree measure

π/3 = π/180 × Degree measure

π/3 × 180/π = Degree measure

π/π × 180/3 = Degree measure

1 × 60 = Degree measure

60 = Degree measure

Degree measure = 60

∴ π/3 radian = 60°

####
**
Convert
**
**
π
**
**
/4
**
**
radians into degree
**

Radian measure = π/180 × Degree measure

π/4 = π/180 × Degree measure

π/4 × 180/π = Degree measure

π/π × 180/4 = Degree measure

1 × 45 = Degree measure

45 = Degree measure

Degree measure = 45

∴ π/4 radian = 45°

####
**
Convert
**
**
π
**
**
/2
**
**
radians into degree
**

Radian measure = π/180 × Degree measure

π/2 = π/180 × Degree measure

π/2 × 180/π = Degree measure

π/π × 180/2 = Degree measure

1 × 90 = Degree measure

90 = Degree measure

Degree measure = 90

∴ π/2 radian = 90°

####
**
Convert
**
**
1 radians into degree
**

Radian measure = π/180 × Degree measure

1 = π/180 × Degree measure

180/π = Degree measure

Degree measure = 180/π

∴ 1 radian = 180/π °

In some cases, we have to divide and convert degrees into minutes. Check this question

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