Question

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

• 825°

a positive angle less than 360° that is coterminal with - 825° is □°.

Explanation:

Step1: Divide by 360

We know that coterminal angles differ by a multiple of 360°. Let's find out how many full - rotations we can make from - 825°. Divide - 825 by 360: $-825\div360 = - 2\frac{105}{360}=-2\frac{7}{24}$.

Step2: Add multiples of 360

We want a positive angle less than 360°. We start adding 360° to - 825°. First, add 360° twice: $-825 + 360\times3=-825 + 1080$.

Step3: Calculate the result

$-825+1080 = 255$.

Answer:

255