Question

Which angle does not appear to have a measure of 23 degrees?

Answer 1

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 $\alpha \neq 23^{\circ}$, 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 $0^{\circ}$ while the second ray lies on angle $23^{\circ}$. Then:

$\alpha=23^{\circ}-0^{\circ}=23^{\circ}$

This angle measures 23 degrees.

Case G.

The first ray lies on angle $87^{\circ}$ while the second ray lies on angle $110^{\circ}$. Then:

$\alpha=110^{\circ}-87^{\circ}=23^{\circ}$

This angle measures 23 degrees.

Case H.

The first ray lies on angle $57^{\circ}$ while the second ray lies on angle $85^{\circ}$. Then:

$\alpha=85^{\circ}-57^{\circ}=28^{\circ}$

This angle doesn't measure 23 degrees.

Case J.

The first ray lies on angle $105^{\circ}$ while the second ray lies on angle $128^{\circ}$. Then:

$\alpha=128^{\circ}-105^{\circ}=23^{\circ}$

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.