**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
and
are both right angles must be false.

**Step 8:** Therefore, ΔLMN has at most one right angle.