Given a right triangle where $m\angle ABC$ is one of the angles, which of the following could be the measure of $m\angle ABC$?

• A. $m\angle ABC=67°$
• B. $m\angle ABC=60°$
• C. $m\angle ABC=127°$
• D. $m\angle ABC=120°$

Answer: (B)

Verified step by step guidance

1. Recall that in a right triangle, one angle is exactly 90\(\degree\), and the other two angles must add up to 90\(\degree\) because the sum of all angles in any triangle is 180\(\degree\).
2. Identify that the angle \( m\angle ABC \) must be one of the two non-right angles, so its measure must be less than 90\(\degree\).
3. Evaluate each given angle option to see if it is less than 90\(\degree\), since any angle greater than or equal to 90\(\degree\) cannot be one of the acute angles in a right triangle.
4. Recognize that angles 127\(\degree\) and 120\(\degree\) are greater than 90\(\degree\), so they cannot be the measure of \( m\angle ABC \) in a right triangle.
5. Conclude that the only possible measure for \( m\angle ABC \) from the given options is 60\(\degree\), as it is less than 90\(\degree\) and fits the properties of angles in a right triangle.