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.
180°
answer
fraction: 180° = of a semicircle
angle measure: 180° = radians
submit answer
π

Explanation:

Step1: Determine the fraction of the semicircle

A semicircle has an angle measure of \( 180^\circ \). So, to find what fraction \( 180^\circ \) is of a semicircle, we divide \( 180^\circ \) by the measure of a semicircle (\( 180^\circ \)):
\( \frac{180^\circ}{180^\circ} = 1 \)

Step2: Convert \( 180^\circ \) to radians

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

Answer:

Fraction: \( 180^\circ = \boxed{1} \) of a semicircle
Angle measure: \( 180^\circ = \boxed{\pi} \) radians