For context, there's a parallelogram with 4 points, top left is X, top right is Y, bottom left is W, and bottom right is Z

Question

In parallelogram WXYZ, the interior angle at point Y measures 30 degrees. What is the measure of the interior angle at point X?

150 degrees
60 degrees
30 degrees
330 degrees

Answer 1

In a parallelogram, opposite angles are equal and adjacent angles are supplementary (i.e., they add up to 180 degrees).

Given that the interior angle at point Y measures 30 degrees, we can find the measure of the angle at point X as follows:

1. Since angles Y and X are adjacent angles, we can use the supplementary property: \[ \text{Angle X} + \text{Angle Y} = 180^\circ \] \[ \text{Angle X} + 30^\circ = 180^\circ \]

2. 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 degrees.