Final answer:
To find angle VZY in kite WXYZ, subtract the sum of angles WXY (104°) and VYZ (49°) from 180°, resulting in angle VZY being 27°.
Step-by-step explanation:
The question requires solving for an angle within kite WXYZ. Given that angle WXY is 104° and angle VYZ is 49°, we can find angle VZY. Since WXYZ is a kite, we know that it has two pairs of adjacent sides that are equal. In this case, we assume XY to be the line of symmetry dividing the kite into two congruent right triangles, XYZ and VWX.
The sum of angles in a triangle equals 180°. In triangle XYZ, angle WXY is 104° and VYZ is 49°. Therefore, to find angle VZY, we subtract the sum of angles WXY and VYZ from 180°:
180° - (104° + 49°) = 180° - 153° = 27°.
Hence, angle VZY is 27°.