The correct answer is:
C) 45.
Explanation:
An angle of measure \(\frac{2\pi}{N}\) can be trisected if and only if N is not divisible by 3.
A 45° angle in radians is \(\frac{\pi}{4}\). Setting up a proportion, we can find the value of N to determine if this fits:
\(\frac{\pi}{4}=\frac{2\pi}{N}\)
Cross multiply:
\(\pi \times N = 4 \times 2\pi
\\
N\pi = 8\pi\)
This means N = 8, and is not divisible by 3; thus the 45 degree angle is trisectible.
