In triangle MNO, angle MNO measures $112°$. If triangle MNO is a right triangle with the right angle at vertex N, what is the measure of angle LMN?

• A. $90°$
• B. $112°$
• C. $68°$
• D. $78°$

Answer: (C)

Verified step by step guidance

1. Identify the given information: triangle MNO is a right triangle with the right angle at vertex N, so angle N measures 90°.
2. Recall that the sum of the interior angles in any triangle is 180°, so we have the equation: \(\angle M + \angle N + \angle O = 180^\circ\).
3. Substitute the known values into the equation: \(\angle M + 90^\circ + 112^\circ = 180^\circ\).
4. Combine the known angles: \(90^\circ + 112^\circ = 202^\circ\), so the equation becomes \(\angle M + 202^\circ = 180^\circ\).
5. Solve for \(\angle M\) by subtracting 202° from both sides: \(\angle M = 180^\circ - 202^\circ\).