In quadrilateral WXYZ, m<W = 42°, mLX = 138°, m2Y= 42°. Find m2Z.

Question

Is WXYZ a parallelogram? Explain your reasoning.

Answer 1

To find m2Z, we can use the fact that the sum of the angle measures in a quadrilateral is 360 degrees.

m<W + mLX + m2Y + m2Z = 360°
42° + 138° + 42° + m2Z = 360°

Simplifying the equation:

m2Z = 360° - 42° - 138° - 42°
m2Z = 138°

So, m2Z is 138 degrees.

Now, to determine if WXYZ is a parallelogram, we need to consider the opposite angles. In a parallelogram, opposite angles are congruent.

The given information does not provide any information about the opposite angles of W and Z, or X and Y. Therefore, we cannot conclude that WXYZ is a parallelogram based on the given information.