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.
280°

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) =(280)/(180) =(2*2*7*10)/(2*2*3*3*5) =(7*10)/(3*3*5) =(70)/(45)=(14)/(9)`

Answer: The angle 280 degrees covers 14/9 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
`280*(\pi )/(180) =(28)/(18)*\pi =(28\pi )/(18)=(2*14*\pi )/(2*9) =(14\pi )/(9)`

Answer: The angle 280 degrees in radians is
`\frac{14\pi} {9}` which in terms of
`\pi` is

14/9

Hope that helps!