A parallelogram has one angle that measures 54°. What are the measures of the other three angles in the parallelogram?
Since opposite angles in a parallelogram are congruent, the opposite angle to the 54° angle also measures 54°. Therefore, the sum of the other two angles must be 180° - 54° - 54° = 72°. Since opposite angles in a parallelogram are also supplementary, the other two angles are congruent as well. Thus, each of the other two angles measures (72°)/2 = 36°. Therefore, the measures of the other three angles in the parallelogram are 54°, 54°, and 36°.
In a parallelogram, opposite angles are equal. Since one angle measures 54°, another angle in the parallelogram that is opposite to it will also measure 54°.
So, the measures of the other three angles in the parallelogram are:
- Angle opposite to the 54° angle: 54°
- Angle adjacent to the 54° angle: 180° - 54° = 126° (since the sum of the adjacent angles in a parallelogram is 180°)
- Angle opposite to the 126° angle: 54°
Therefore, the measures of the other three angles in the parallelogram are 54°, 126°, and 54°.