Question

1. since a full circumference is 360 times as long as $\frac{1}{360}$ of its length, an angle measuring $60^{\circ}$ subtends an arc on any circle centered at its vertex that is: times as large as the circles circumference or preview enter a mathematical expression more... try again. what does it mean if the angle measures $60^{\circ}$? how is this related to the proportion of a circles circumference the angle subtends if the circle is centered at the angles vertex? 16.7 percent of the circles circumference preview try again. once you get the previous part completed correctly, how do you turn a ratio comparison into a percentage comparison? u knowing that an angle measuring $2\pi$ radians subtends the entire circumference of any circle centered at its vertex, an angle measuring $60^{\circ}$ measures how many radians? $\frac{pi}{3}$ radians preview correct! the angle measure in radians is $(\frac{60}{360})(2\pi)$, or about 1.0472. b. another angle has a measure of $340^{\circ}$. what is the measure of this angle in radians? 5.93 radians preview correct! the angle measure in radians is $(\frac{340}{360})(2\pi)$, or about 5.9341. c. another angle has a measure of $155^{\circ}$. what is the measure of this angle in radians? 2.71 radians preview * try again. what proportion or percentage of the circles circumference does this angle subtend? the angle measure in radians will be this same proportion of $2\pi$ radians.

Explanation:

Step1: Convert degree to radian formula

The formula to convert degrees to radians is \( \text{Radians}=\frac{\theta}{360}\times2\pi\), where \(\theta\) is the angle in degrees.

Step2: Substitute \(\theta = 155^{\circ}\) into the formula

When \(\theta = 155^{\circ}\), we have \( \text{Radians}=\frac{155}{360}\times2\pi\).
Simplify \(\frac{155}{360}\times2\pi=\frac{155\pi}{180}=\frac{31\pi}{36}\approx2.71\)

Answer:

\(\frac{31\pi}{36}\approx2.71\) radians