Answer:
[tex]c)\ 45^\circ[/tex]
Step-by-step explanation:
Given
A semicircle divided into 8 parts
Required
Angle that can be measured with the piece
First, we calculate the minimum angle that can be calculated.
[tex]\theta =\frac{Semi\ circle}{8}[/tex]
[tex]Semicircle = 180^\circ[/tex]
So, we have:
[tex]\theta =\frac{180^\circ}{8}[/tex]
[tex]\theta =22.5^\circ[/tex]
This implies that all angles that can be measured using the piece must be a multiple of 22.5 not greater than 180 degrees (i.e. not greater than the semicircle)
So, we have:
[tex]\theta =22.5^\circ,\ 45^\circ,\ 67.5^\circ,\ 90^\circ,\ 112.5^\circ,\ 135^\circ,\ 157.5^\circ,\ 180^\circ[/tex]
From the list of options, only 45 degrees appear in the possible values of [tex]\theta[/tex]
Hence:
[tex]\theta = 45^\circ[/tex]
