Question

find the angle of the least positive measure (in degrees, not equal to the given measure) that is coterminal with a. a = - 432° the measure is (square^{circ}).

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles are found by adding or subtracting multiples of 360°. We want to find a positive coterminal angle for - 432°. Let the coterminal angle be $\theta=-432^{\circ}+k\cdot360^{\circ}$, where $k$ is an integer.

Step2: Find the value of $k$ for the least - positive coterminal angle

We start with $k = 1$. $\theta=-432^{\circ}+1\times360^{\circ}=-72^{\circ}$, which is negative. When $k = 2$, $\theta=-432^{\circ}+2\times360^{\circ}=-432^{\circ}+720^{\circ}=288^{\circ}$.

Answer:

$288$