To convert degree measure to radian measure, we have to use the formula given below.

Radians = (π/180) x (Degree Measure)

Let us look at some examples to understand how to convert degree measures to radian measures.

**Example 1 :**

Convert 25° into radian measure.

**Solution :**

Formula to convert degree measure to radian measure is

= (π/180) x degree measure

= (π/180) x 25

= 5π / 36 radians

**Example 2 :**

Convert 240° into radian measure

**Solution :**

Formula to convert degree measure to radian measure is

= (π/180) x degree measure

= (π/180) x 240

= 4π / 3 radians

**Example 3 :**

Convert 520° into radian measure.

**Solution :**

Formula to convert degree measure to radian measure is

= (π/180) x degree measure

= (π/180) x 520

= 26π / 9 radians

**Example 4 :**

Convert 40° 20' to radian measure.

**Solution :**

To convert 40° 20' to radian measure, first we have to convert 20' to degree.

To convert 20' to degree, we have to divide it by 60.

20' = (20/60)°

20' = (1/3)°

Then,

40° 20' = (40 + 1/3)°

40° 20' = (121/3)°

Formula to convert degree measure to radian measure is

= (π/180) x degree measure

= (π/180) x (121/3)

= (121π/540) radians

**Example 5 :**

Convert -47° 30' into radian measure

**Solution :**

To convert -47° 30' to radian measure, first we have to convert 30' to degree.

To convert 30' to degree, we have to divide it by 60.

30' = (30/60)°

30' = (1/2)°

Then,

-47° 30' = -(47 + 1/2)°

-47° 30' = (95/2)°

Formula to convert degree measure to radian measure is

= (π/180) x degree measure

= (π/180) x (95/2)

= 19π / 72 radians

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