Question

Please help! What fractional part of one semicircle does the labeled angle represent? Express

your answer as a fraction in simplest terms. Then, express the labeled angle in radian
measure,
100'

Answer 1

Let's consider what the problem wants us to find:

• fractional part covered by the labeled angle

• angle in radians

Let's find the fractional part:

⇒ the fractional part is equal:

`(degree-covered-by-angle)/(total-angle) =(100)/(180) =(2*2*5*5)/(2*2*3*3*5) =(5)/(3*3) =(5)/(9)`

Answer: The angle 100 degrees covers 5/9 of a semicircle.

Let's find the angle measure in radians:

⇒ we know that
`2\pi` radians are equal to 360 degrees

⇒ to convert any degree to radians, you must multiply
`(\pi )/(180)`

so
`100*(\pi )/(180) =(100\pi )/(180) =(10)/(18) \pi =(5)/(9) \pi`

Answer: The angle 100 degrees in radians is
`(5)/(9) \pi` which in terms of
`\pi` is

5/9

Hope that helps!