In a parallelogram, the opposite angles are equal, and consecutive angles are supplementary (they add up to 180 degrees).
Let's denote the angles of the parallelogram as follows:
- Angle M (top left corner)
- Angle J (bottom left corner)
- Angle K (top right corner)
- Angle L (bottom right corner)
From the problem:
- Angle M = 140° (inside top left corner)
Given that opposite angles are equal and consecutive angles are supplementary, we can find the unknown angles:
-
Since angle M = 140°, then angle K (opposite to M) is also 140°.
-
Now, considering that angle M and angle J are consecutive angles, we can determine angle J: \[ M + J = 180° \] \[ 140° + J = 180° \] \[ J = 180° - 140° = 40° \]
-
Since angle J and angle L are opposite angles, angle L will also be 40°.
-
Finally, angle L is consecutive with angle K, so: \[ L + K = 180° \] \[ 40° + K = 180° \] \[ K = 180° - 40° = 140° \]
Since we are looking for angle L, and we've already identified that it is 40°, the angles of the parallelogram are:
- M = 140°
- J = 40°
- K = 140°
- L = 40°
However, you mentioned an unknown angle inside (the bottom right corner). If we follow the relative position and same logic, since angle J is 40°, it does not appear as on the list given (100°, 140°, 30°, 135°).
Among the options provided, the answer corresponding to angle K (inside bottom right corner), which makes sense contextually and numerically with provided values, is:
- 40° (but it isn’t in your options, suggesting the question aims for an angle related/remains)
If, however, we have to deduce which of those choices could relate to the identified angles, then none match, but if the context remained unresolved, please provide further clarifications or typos in question listed suggestions.
This analysis revolves strictly around the sequential checks therein stated. Would you like to proceed with further adjustments or clarifications?