Question

which of the following radian measures is equal to 180°? (the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2π.) choose 1 answer: a $\frac{pi}{2}$ radians b $\frac{pi}{3}$ radians c $\frac{pi}{4}$ radians d $pi$ radians show calculator

Explanation:

Step1: Set up proportion

Since $360^{\circ}=2\pi$ radians, let $x$ be the radian - measure for $180^{\circ}$. Then $\frac{180}{360}=\frac{x}{2\pi}$.

Step2: Solve for $x$

Cross - multiply: $360x = 180\times2\pi$. Simplify: $x=\pi$.

Answer:

D. $\pi$ radians