One angle of a parallelogram measures 42°. 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 42° angle also measures 42°. Therefore, the two opposite angles are both 42°.
The sum of the angles in a parallelogram is 360°. If we subtract the two congruent 42° angles, we are left with 276° for the other two angles.
Since opposite sides in a parallelogram are parallel, the other two angles are also congruent. Therefore, we can divide the 276° by 2 to get the measure of each of these angles:
276°/2 = 138°
So the other three angles in the parallelogram each measure 138°.
In a parallelogram, opposite angles are congruent. Since one angle of the parallelogram measures 42°, the opposite angle will also measure 42°.
Therefore, the measures of the other three angles in the parallelogram are:
- The angle opposite to the given angle is 42°.
- The adjacent angle of the given angle will also measure 42°.
- The other two angles opposite to the adjacent angles will also measure 42° each.