Short Answer 
The total interior angle of a parallelogram is 360°, calculated using the formula 180°(n-2) for n=4 sides. By setting up the angles and solving the equation, we find that angle O measures 105° when x is determined to be 35°.
Step 1: Understanding the Interior Angles
The total interior angle of a parallelogram is always 360°, which can be calculated using the formula 180°(n-2), where n is the number of sides. In the case of a parallelogram, which has 4 sides, the calculation becomes 180°(4-2), resulting in 360°.
Step 2: Setting Up the Equation
In a parallelogram, opposite angles are equal. Hence, if we denote angles as follows: angle L = angle N and angle O = angle M, we can represent their measures as:
- angle L = x + 40°
- angle N = x + 40°
- angle O = 3x
- angle M = 3x
This provides us with the equation: (x + 40°) + (x + 40°) + (3x) + (3x) = 360°.
Step 3: Solving for Angle O
Combining like terms from the equation leads us to 8x + 80° = 360°. To isolate x, we subtract 80° from both sides, resulting in 8x = 280°. Dividing by 8, we find that x = 35°. This allows us to calculate angle O as 3x = 3(35°) = 105°.