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

Answer:

$\theta=162^0$

Step-by-step explanation:

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

Circumference of the Circle =10

$\text{If the length of an arc}=\dfrac{9}{2}$

$\text{Length of an arc}=\dfrac{\theta}{360}X2\pi r$

Therefore:

$\dfrac{9}{2}=\dfrac{\theta}{360}X10\\\dfrac{\theta}{360}=\dfrac{9}{2}\div 10\\\dfrac{\theta}{360}=\dfrac{9}{20}\\ Cross Multiply\\20\theta=9X360\\\theta=(9X360)\div 20\\\theta=162^0$

The central angle of the arc is 162 degrees.

Answer 2

Answer:

Its 9\2

Step-by-step explanation:

I found it on Khan