Given that line zx bisects angle $\angle wzy$ in triangle wzy, and the measure of angle $\angle yxz$ is $6m-12$ degrees, which of the following could be the value of $m$ if angle $\angle yxz$ is an acute angle?

• A. $6$
• B. $5$
• C. $3$
• D. $4$

Answer: (D)

Verified step by step guidance

1. Identify the given angle expression: the measure of angle \( \angle yxz \) is given as \( 6m - 12 \) degrees.
2. Recall that an acute angle is an angle whose measure is greater than 0 degrees and less than 90 degrees.
3. Set up the inequality to represent the condition for \( \angle yxz \) being acute: \( 0 < 6m - 12 < 90 \).
4. Solve the compound inequality step-by-step: first, solve \( 6m - 12 > 0 \) to find the lower bound for \( m \), then solve \( 6m - 12 < 90 \) to find the upper bound for \( m \).
5. Determine which of the given values for \( m \) satisfy the inequality, thus making \( \angle yxz \) an acute angle.