Question

Two angles that can be trisected with a straightedge and compass are a 90angle and a _____ angle.

A. 9
B. 75
C. 45
D. 90

Answer 1

the answer on apex is 45°

Answer 2

The correct answer is:

C) 45.

Step-by-step explanation:

An angle of measure
`(2\pi)/(N)` can be trisected if and only if N is not divisible by 3.

A 45° angle in radians is
`(\pi)/(4)`. Setting up a proportion, we can find the value of N to determine if this fits:


`(\pi)/(4)=(2\pi)/(N)`

Cross multiply:


`\pi * N = 4 * 2\pi \\ N\pi = 8\pi`

This means N = 8, and is not divisible by 3; thus the 45 degree angle is trisectible.