The opposite angles of a parallelogram are congruent. The adjacent angles are supplementary. If angle X measures 110 degrees, then what are the measures of angle Y and angle Z?
Y = 180 - 110 = 70deg.
Z = 180 = 70 = 110deg
Y=180-110=70deg
Z=180-70=110deg
Thanks for your help Ian
Y=180-110=70°
Z=180-70=110
thanks for the help Henry
To find the measures of angles Y and Z, we first need to understand the properties of a parallelogram.
In a parallelogram:
- Opposite angles are congruent, meaning they have the same measure.
- Adjacent angles are supplementary, meaning their measures add up to 180 degrees.
Since we know angle X measures 110 degrees, it is one of the adjacent angles.
To find angle Y, we need to determine its relationship with angle X.
Since angle X and angle Y are adjacent angles, they are supplementary. Therefore, we can find the measure of angle Y by subtracting angle X from 180 degrees.
angle Y = 180 degrees - angle X
angle Y = 180 degrees - 110 degrees
angle Y = 70 degrees
So, angle Y measures 70 degrees.
Now, to find angle Z, we use the fact that opposite angles in a parallelogram are congruent.
angle X and angle Z are opposite angles, so they have the same measure.
angle Z = angle X = 110 degrees
Therefore, angle Z measures 110 degrees.