When one angle of a triangle is obtuse, it means that angle is greater than 90 degrees. In any triangle, the sum of all three interior angles must equal 180 degrees. Since one angle is already more than 90 degrees, the sum of the other two angles must be less than 90 degrees.
To elaborate, let’s say the obtuse angle is 120 degrees. To find the sum of the other two angles, we would calculate:
Sum of other angles = Total sum of angles – Obtuse angle
Sum of other angles = 180 degrees – 120 degrees = 60 degrees
Thus, the sum of the measures of the other two angles must be less than 90 degrees in order for their total, when added to the obtuse angle, to equal 180 degrees. This confirms that if one angle is obtuse, the sum of the measures of the remaining angles must be less than 90 degrees.