Question

question 9 of 10
identify the correct phrase to complete the statement.
a central angle has a measure of 1 radian if:
a. the radius has a length of 1.
b. the central angle is 90°.
c. the length of the arc it intercepts is twice the length of the radius.
d. the length of the arc it intercepts is the same as the length of the radius.

Explanation:

The definition of a radian states that a central angle measures 1 radian when the length of the arc it intercepts equals the radius of the circle. Option A is incorrect because radius length alone doesn’t define the angle measure. Option B is incorrect because 90° equals π/2 radians, not 1 radian. Option C is incorrect because it describes an arc length twice the radius (which would be 2 radians). Option D matches the definition.

Answer:

D. the length of the arc it intercepts is the same as the length of the radius.