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