Question

A circle has a circumference of 10\blue{10} 10 start color #6495ed, 10, end color #6495ed . It has an arc of length 92\dfrac{9}{2} 2 9 ​ start fraction, 9, divided by, 2, end fraction . What is the central angle of the arc, in degrees? ∘^\circ ∘ degrees

Answer 1

Its 9\2

Explanation:

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Answer 2

`\theta=162^0`

Explanation:

`\text{Circumference of a circle}=2\pi r`

Circumference of the Circle =10

`\text{If the length of an arc}=(9)/(2)`

`\text{Length of an arc}=(\theta)/(360)X2\pi r`

Therefore:

`(9)/(2)=(\theta)/(360)X10\\(\theta)/(360)=(9)/(2)/ 10\\(\theta)/(360)=(9)/(20)\\$Cross Multiply\\20\theta=9X360\\\theta=(9X360)/ 20\\\theta=162^0`

The central angle of the arc is 162 degrees.