Question

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.Please fill in both blanks and clarify which awnser goes in which blank.

Answer 1

Recall that a semicircle is formed by a central angle with measure 180 degrees, therefore, the given angle represents:

`(285)/(180)=(19)/(12)`

of a semicircle.

Now, recall that the central angle of one semicircle measures:

`\pi\text{radians.}`

Therefore:

`285^(\circ)=(19)/(12)\pi\text{ radians.}`

Answer:

`\begin{gathered} \text{Fraction: 285}^(\circ)=(19)/(12)\text{ of a semicircle.} \\ \text{Angle measure: 285}^(\circ)=(19)/(12)\pi\text{ radians.} \end{gathered}`