Finding the Measure of Angle WYX in a Rhombus
The image shows a geometric figure labeled WXYZ, which is identified as a rhombus. There is an angle at vertex Y that is marked as 75 degrees. The question asks for the measure of the angle ∠WYX.
In a rhombus, opposite angles are equal and adjacent angles are supplementary (meaning they add up to 180 degrees). Since the angle at vertex Y is given as 75 degrees, the angle at vertex W (which is adjacent to angle Y) would be supplementary to it. Therefore, to find the measure of angle W (∠WYX), we need to subtract the angle at vertex Y from 180 degrees:
∠WYX = 180 degrees - ∠Y = 180 degrees - 75 degrees = 105 degrees
So the measure of angle ∠WYX is 105 degrees.
