Explanation: The rhombus has two pairs of parallel sides and opposite angles that are equal. Therefore, angle X is equal to angle Z, and angle Y is equal to angle W. Since the opposite angles of a rhombus are equal, we know that angle Y is equal to angle A.
Using the fact that the sum of the angles in a quadrilateral is 360 degrees, we can set up the following equation:
X + Y + Z + W = 360
Substituting the known angles, we get:
X + A + Z + Y = 360
Simplifying, we get:
2X + 2Y = 360
Dividing by 2, we get:
X + Y = 180
Substituting Y = A, we get:
X + A = 180
Substituting the value of angle A, we get:
X + 38 = 180
Solving for X, we get:
X = 142
Therefore, angle X is equal to 142 degrees.
Since angle Y is equal to angle A, we know that angle Y is also equal to 38 degrees. Therefore, angle Y is equal to 38 degrees.
Hopefully this helpsss