Answer:
Correct option: H
Explanation:
In each case we have a protractor and two rays that meet at the center of the protractor. So let's call the α the angle between the two rays, then if in one case [tex]\alpha \neq 23^{\circ}[/tex], the that angle will not appear to have a measure of 23 degrees. In order to solve this problem let's check each case:
Case F.
The first ray lies on angle [tex]0^{\circ}[/tex] while the second ray lies on angle [tex]23^{\circ}[/tex]. Then:
[tex]\alpha=23^{\circ}-0^{\circ}=23^{\circ}[/tex]
This angle measures 23 degrees.
Case G.
The first ray lies on angle [tex]87^{\circ}[/tex] while the second ray lies on angle [tex]110^{\circ}[/tex]. Then:
[tex]\alpha=110^{\circ}-87^{\circ}=23^{\circ}[/tex]
This angle measures 23 degrees.
Case H.
The first ray lies on angle [tex]57^{\circ}[/tex] while the second ray lies on angle [tex]85^{\circ}[/tex]. Then:
[tex]\alpha=85^{\circ}-57^{\circ}=28^{\circ}[/tex]
This angle doesn't measure 23 degrees.
Case J.
The first ray lies on angle [tex]105^{\circ}[/tex] while the second ray lies on angle [tex]128^{\circ}[/tex]. Then:
[tex]\alpha=128^{\circ}-105^{\circ}=23^{\circ}[/tex]
This angle measures 23 degrees.
Conclusion: The angle that will not appear to have a measure of 23 degrees is the one for case H.
