Question

find a positive angle less than 360° that is coterminal with the given angle. - 1030° a positive angle less than 360° that is coterminal with - 1030° is °

Explanation:

Step1: Divide by 360

Divide - 1030 by 360: $\frac{-1030}{360}=-2\frac{310}{360}=-2-\frac{31}{36}$.

Step2: Find the multiple of 360

We want to add multiples of 360 to - 1030 to get a positive angle less than 360. Let's find the smallest non - negative integer $n$ such that $-1030 + 360n>0$.
We start by adding 360 repeatedly.
$-1030+3\times360=-1030 + 1080$.

Step3: Calculate the coterminal angle

$-1030+3\times360 = 50$.

Answer:

$50$