## A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the arc is ?

Question

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## Answers ( )

Answer: 320°

Step-by-step explanation:

This is a circle geometry.

The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

Now the length of an arc of a circle is

Arc length = πr0°/180° or 2πr0°/360°

To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

πr0° = 8π × 180

0°. = 8π × 180

———–

π × r

= 8 × 180. 8 × 180

——– or ———

9/2. 4.5

= 8 × 180 × 2

————

9

= 8 × 20 × 2

= 320°

or 8 × 180/4.5

= 1440/4.5

= 320°