Question

find a positive angle less than 360° that is coterminal with the given angle. - 995° a positive angle less than 360° that is coterminal with - 995° is \\(\square\\)°.

Explanation:

Step1: Find total rotations to add

Coterminal angles differ by multiples of $360^\circ$. Calculate how many full $360^\circ$ rotations are needed to make $-995^\circ$ positive and less than $360^\circ$.
First, find the smallest integer $n$ such that $-995 + 360n > 0$.
Solve for $n$: $360n > 995$ → $n > \frac{995}{360} \approx 2.76$. So $n=3$.

Step2: Calculate coterminal angle

Add $3 \times 360^\circ$ to $-995^\circ$.
$3 \times 360^\circ = 1080^\circ$
$-995^\circ + 1080^\circ = 85^\circ$

Step3: Verify the result

Check that $0^\circ < 85^\circ < 360^\circ$, which satisfies the requirement.

Answer:

$85$