What is the radian measure of an angle of x degrees?

Solution:

The radian is an S.I. unit that is used to measure angles. One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle.

1 radian is defined as the angle subtended at the centre of a unit circle by a unit arc length on the circumference.

An arc length of 't' units subtends an angle measure of 't' radians at the center of the circle as shown in the diagram below. 

Since the circumference of a unit circle is 2π units, we have,

360^º = 2π radians

⇒ 180^º = π radians

Hence, one radian is equal to 180 / π degrees, which is approximate 57.3^º

Thus, we have the conversion formulas as follows:

• Multiply the angle by π /180 to convert from degrees to radians.

• Multiply the angle by 180/ π to convert from radians to degrees.

To convert x degrees to radian we will multiply x with π /180

Thus, x degrees = x. π /180 radians

Therefore, the radian measure of an angle of x degrees is equal to \(\text{x}\) π / 180 radians.

What is the radian measure of an angle of x degrees?

Summary:

The radian measure of an angle of x degrees is equal to x × π / 180 radians.