Step 1: Assume ΔLMN has more than one right angle. That is, assume that angle L and angle M are both right angles.
Step 2: If M and N are both right angles, then
Step 3: [The sum of the measures of the angles of a triangle is 180.]
Step 4: Substitution gives
Step 5: Solving gives
Step 6: This means that there is no ΔLMN, which contradicts the given statement.
Step 7: So, the assumption that
are both right angles must be false.
Step 8: Therefore, ΔLMN has at most one right angle.