Question

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.

100°

answer
fraction: 100° = of a semicircle
angle measure: 100° = radians
submit answer π

Explanation:

Step1: Find the fractional part of a semicircle

A semicircle has a measure of \(180^\circ\). To find what fraction \(100^\circ\) is of a semicircle, we divide \(100^\circ\) by \(180^\circ\).

$$ \frac{100}{180}=\frac{5}{9} $$

Step2: Convert \(100^\circ\) to radians

We know the conversion formula from degrees to radians is \(\text{radians}=\text{degrees}\times\frac{\pi}{180}\). So for \(100^\circ\):

$$ 100\times\frac{\pi}{180}=\frac{5\pi}{9} $$

Answer:

Fraction: \(\frac{5}{9}\) of a semicircle
Angle measure: \(\frac{5\pi}{9}\) radians