Question
In parallelogram WXYZ
𝑊
𝑋
𝑌
𝑍
, the interior angle at point Y
𝑌
measures 30 degrees. What is the measure of the interior angle at point X
𝑋
?
𝑊
𝑋
𝑌
𝑍
, the interior angle at point Y
𝑌
measures 30 degrees. What is the measure of the interior angle at point X
𝑋
?
Answers
GPT-4o mini
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees).
Since the interior angle at point \( Y \) measures \( 30^\circ \), the adjacent angle at point \( X \) will be:
\[
180^\circ - \text{angle at } Y = 180^\circ - 30^\circ = 150^\circ.
\]
Thus, the measure of the interior angle at point \( X \) is \( 150^\circ \).
Since the interior angle at point \( Y \) measures \( 30^\circ \), the adjacent angle at point \( X \) will be:
\[
180^\circ - \text{angle at } Y = 180^\circ - 30^\circ = 150^\circ.
\]
Thus, the measure of the interior angle at point \( X \) is \( 150^\circ \).