Question

find the angle of least positive measure (not equal to the given measure) that is coterminal with the angle 4491°. the measure is □°. (simplify your answer.)

Explanation:

Step1: Recall coterminal angle formula

To find a coterminal angle with a given angle \(\theta\) in degrees, we use the formula \(\theta - 360^{\circ}n\) (where \(n\) is an integer) to get a positive coterminal angle less than \(\theta\). We need to find the largest integer \(n\) such that \(\theta- 360^{\circ}n>0\) and \(\theta - 360^{\circ}n
eq\theta\).

First, divide \(4491\) by \(360\) to find \(n\).
\(n=\lfloor\frac{4491}{360}
floor\) (floor function gives the greatest integer less than or equal to the number)
\(\frac{4491}{360}=12.475\), so \(n = 12\)

Step2: Calculate the coterminal angle

Now, substitute \(\theta = 4491^{\circ}\) and \(n = 12\) into the formula \(\theta-360^{\circ}n\)
\(4491^{\circ}-360^{\circ}\times12\)
First, calculate \(360^{\circ}\times12 = 4320^{\circ}\)
Then, \(4491^{\circ}- 4320^{\circ}=171^{\circ}\)

We check if this is positive and not equal to the original angle (it is, since \(171^{\circ}
eq4491^{\circ}\) and \(171^{\circ}>0\))

Answer:

\(171\)