A parallelogram has one angle that measures 129°. What are the measures of the other three
angles in the parallelogram?
Since opposite angles in a parallelogram are congruent, the opposing angle to the 129° angle is also 129°.
Therefore, the sum of the remaining two angles must add up to 180° since they are adjacent and form a straight line.
Let's call one of these angles "x". Then, we have:
x + (x + 129°) = 180°
Simplifying this equation, we get:
2x + 129° = 180°
Subtracting 129° from both sides, we get:
2x = 51°
Dividing both sides by 2, we get:
x = 25.5°
Therefore, the other two angles in the parallelogram are both 25.5°.
To summarize:
- Two opposite angles are 129° each.
- The other two adjacent angles are 25.5° each.
In a parallelogram, opposite angles are congruent. Since one angle measures 129°, the opposite angle must also measure 129°. Therefore, two angles in the parallelogram have measures of 129° each.
The sum of the measures of the angles in a parallelogram is 360°. Since two angles are already known (129° + 129° = 258°), subtracting this from 360° gives the sum of the measures of the other two angles.
360° - 258° = 102°
Therefore, the measures of the other two angles in the parallelogram are both 102° each.