<h2>
Answer:</h2><h2>
</h2><h3>Correct option: H</h3><h2>
</h2><h2>
Explanation:</h2><h2>
</h2>
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
, the that angle will not appear to have a measure of 23 degrees. In order to solve this problem let's check each case:
<h3>Case F.</h3><h3 />
The first ray lies on angle
while the second ray lies on angle
. Then:
![\alpha=23^{\circ}-0^{\circ}=23^{\circ}](https://tex.z-dn.net/?f=%5Calpha%3D23%5E%7B%5Ccirc%7D-0%5E%7B%5Ccirc%7D%3D23%5E%7B%5Ccirc%7D)
<em>This angle measures 23 degrees.</em>
<h3>Case G.</h3><h3 />
The first ray lies on angle
while the second ray lies on angle
. Then:
![\alpha=110^{\circ}-87^{\circ}=23^{\circ}](https://tex.z-dn.net/?f=%5Calpha%3D110%5E%7B%5Ccirc%7D-87%5E%7B%5Ccirc%7D%3D23%5E%7B%5Ccirc%7D)
<em>This angle measures 23 degrees.</em>
<h3>Case H.</h3><h3 />
The first ray lies on angle
while the second ray lies on angle
. Then:
![\alpha=85^{\circ}-57^{\circ}=28^{\circ}](https://tex.z-dn.net/?f=%5Calpha%3D85%5E%7B%5Ccirc%7D-57%5E%7B%5Ccirc%7D%3D28%5E%7B%5Ccirc%7D)
<em>This angle doesn't measure 23 degrees.</em>
<em></em>
<h3>Case J.</h3><h3 />
The first ray lies on angle
while the second ray lies on angle
. Then:
![\alpha=128^{\circ}-105^{\circ}=23^{\circ}](https://tex.z-dn.net/?f=%5Calpha%3D128%5E%7B%5Ccirc%7D-105%5E%7B%5Ccirc%7D%3D23%5E%7B%5Ccirc%7D)
<em>This angle measures 23 degrees.</em>
Conclusion: The angle that will not appear to have a measure of 23 degrees is the one for case H.