Question
in parallelogram WXYZ, the interior angle at point Y measures 30 degrees. what is the measure of the interior angle at point X?
a. 330 degrees
b. 60 degrees
c. 150 degrees
d. 30 degrees
a. 330 degrees
b. 60 degrees
c. 150 degrees
d. 30 degrees
Answers
GPT-4o mini
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees). Given that the interior angle at point Y measures 30 degrees, we can find the measure of the interior angle at point X, which is adjacent to angle Y.
Since Y and X are adjacent angles:
\[
\text{Angle Y} + \text{Angle X} = 180^\circ
\]
Substituting the value of angle Y:
\[
30^\circ + \text{Angle X} = 180^\circ
\]
Now, solving for angle X:
\[
\text{Angle X} = 180^\circ - 30^\circ = 150^\circ
\]
Therefore, the measure of the interior angle at point X is \(150^\circ\).
The correct answer is **c. 150 degrees**.
Since Y and X are adjacent angles:
\[
\text{Angle Y} + \text{Angle X} = 180^\circ
\]
Substituting the value of angle Y:
\[
30^\circ + \text{Angle X} = 180^\circ
\]
Now, solving for angle X:
\[
\text{Angle X} = 180^\circ - 30^\circ = 150^\circ
\]
Therefore, the measure of the interior angle at point X is \(150^\circ\).
The correct answer is **c. 150 degrees**.