Question

find the angle of the least positive measure (in degrees, not equal to the given measure) that is coterminal with a. a = - 556° the measure is °

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles are given by $\theta + 360^{\circ}n$, where $\theta$ is the given angle and $n$ is an integer. We want to find the least positive coterminal angle of $A=-556^{\circ}$, so we need to find the value of $n$ such that $- 556^{\circ}+360^{\circ}n>0$.

Step2: Solve for $n$

Let's solve the inequality $-556 + 360n>0$. Add 556 to both sides: $360n>556$. Then $n>\frac{556}{360}\approx1.54$. Since $n$ is an integer, the smallest value of $n$ for which the angle is positive is $n = 2$.

Step3: Calculate the coterminal angle

Substitute $n = 2$ into the coterminal - angle formula: $\theta=-556^{\circ}+360^{\circ}\times2$.
$\theta=-556^{\circ}+720^{\circ}=164^{\circ}$.

Answer:

$164$