Question
In parallelogram WXYZ, the interior angle at point Y measures 30 degrees. What is the measure of the interior angle at point X?
(1 point)
330 degrees
60 degrees
30 degrees
150 degrees
(1 point)
330 degrees
60 degrees
30 degrees
150 degrees
Answers
GPT-4o mini
In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Since the interior angle at point Y measures 30 degrees, the angle at point W (which is opposite to angle Y) also measures 30 degrees.
The angles at points X and Y are adjacent, so their measures add up to 180 degrees. Therefore, we can find the measure of angle X as follows:
\[
\text{Angle X} + \text{Angle Y} = 180^\circ
\]
\[
\text{Angle X} + 30^\circ = 180^\circ
\]
\[
\text{Angle X} = 180^\circ - 30^\circ = 150^\circ
\]
Thus, the measure of the interior angle at point X is **150 degrees**.
The angles at points X and Y are adjacent, so their measures add up to 180 degrees. Therefore, we can find the measure of angle X as follows:
\[
\text{Angle X} + \text{Angle Y} = 180^\circ
\]
\[
\text{Angle X} + 30^\circ = 180^\circ
\]
\[
\text{Angle X} = 180^\circ - 30^\circ = 150^\circ
\]
Thus, the measure of the interior angle at point X is **150 degrees**.