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Masteriza [31]
3 years ago
11

Karen correctly solved

Mathematics
1 answer:
Sonja [21]3 years ago
7 0

Answer

d

Step-by-step explanation:

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Arc CD is 2/3 of the circumference of a circle. What is the radian measure of the central angle?
Butoxors [25]

⁴/₃π radian

<h3>Further explanation</h3>

Given:

Arc CD is  \frac{2}{3} of the circumference of a circle.

We will measure the central angle of the circle in radians.

Step-1: measure the central angle (θ) in degrees

The full angle of a circle is 360°, thus

\boxed{ \ \theta = \frac{2}{3} \times 360^0 \ }

We get the degree measure of the middle angle, i.e., \boxed{ \ \theta = 240^0 \ }

Step-2: convert degrees to radians

Because \boxed{ \ \pi \ radian = 180^0 \ }, then

\boxed{ \ \theta = 240^0 \times \frac{\pi \ radians}{180^0} \ }

Cross out 240° and 180° because they are equally divided by 60°.

\boxed{ \ \theta = 4 \times \frac{\pi \ radians}{3} \ }

Hence, the radian measure of the central angle is \boxed{\boxed{ \ \theta = \frac{4}{3} \pi \ radians \ }}

- - - - - - -

Quick Steps

The full angle of a circle is 2π radians.

\boxed{ \ \theta = \frac{2}{3} \times 2 \pi \ radians \ }

Hence, the radian measure of the central angle is \boxed{\boxed{ \ \theta = \frac{4}{3} \pi \ radians \ }}

One radian represents the measure of a central angle of a circle that intercepts an arc whose length equals a radius of the circle.

<h3>Learn more</h3>
  1. What is 270° converted to radians brainly.com/question/3161884
  2. The general form of the equation of circle with center A(-3,12) and the radius is 5 brainly.com/question/1506955
  3. The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)?  brainly.com/question/1952668

Keywords: arc CD is 2/3 of the circumference of a circle, what is the radian measure of the central angle, converts, pi, π, the full angle

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Step-by-step explanation:

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