Question

point p is in the interior of ∠mno. benito wrote the equation ∠mnp + ∠pno = ∠mno. explain benito’s error.

choose the correct answer.

○ a. benito used the wrong notation in the equation showing the relationship between the angle measures. the correct equation is m∠mnp + m∠pno = m∠mno
○ b. benito did not show the relationship between the angles correctly. the correct equation is ∠mnp + ∠mno = ∠pno
○ c. benito used the wrong notation in the equation, and he did not show the relationship between the angle measures correctly. the correct equation is m∠mno + m∠pno = m∠mnp
○ d. benito used the wrong notation in the equation, and he did not show the relationship between the angle measures correctly. the correct equation is m∠mnp + m∠pno = m∠mnp
○ e. benito did not show the relationship between the angles correctly. the correct equation is ∠mno + ∠pno = ∠mnp

Explanation:

To determine Benito's error, we analyze the angle addition postulate. When a point \( P \) is inside \( \angle MNO \), the sum of the measures of the two smaller angles (\( \angle MNP \) and \( \angle PNO \)) should equal the measure of the larger angle (\( \angle MNO \)).

• Benito used \( \angle MNP + \angle PNO = \angle MNO \), but angle notation without "m" (for measure) is incorrect here. We need to use the measure of the angles (denoted by \( m\angle \)) to show the relationship of their sizes.
• Option A states that Benito used the wrong notation (no "m" for angle measures) and the correct equation is \( m\angle MNP + m\angle PNO = m\angle MNO \), which matches the angle addition postulate.
• Other options have incorrect angle relationships (e.g., B, C, D, E propose wrong sums or incorrect angle combinations).

Answer:

A. Benito used the wrong notation in the equation showing the relationship between the angle measures. The correct equation is \( m\angle MNP + m\angle PNO = m\angle MNO \)