1. **State the problem:** We are given a rhombus WXYZ with given angles: angle XYZ = 65°, angle WXK = 65°, angle XKY = 65°, and angle KXY = 30°. We need to find the measures of angles VWY and WXY (assuming a typo and 'vwy' means 'WYZ' or angles related to the vertices). Since the user mentions positioning hints for angles related to points W, V, Y or W, X, Y, we focus on angle WXY. 2. **Recall properties of a rhombus:** - All sides are equal in length: WX = XY = YZ = ZW. - Opposite angles are equal. - Adjacent angles are supplementary (sum to 180°). 3. **Analyze the given angles in the rhombus:** - angle XYZ = 65° means angle at Y between points X and Z is 65°. - Since adjacent angles in rhombus sum to 180°, angle WXY = 180° - 65° = 115°. 4. **Analyze angles around point K inside the rhombus:** We are given angles WXK = 65°, XKY = 65°, and KXY = 30°. - Triangle WKY has points W, K, Y. - Since WXK and XKY are both 65°, and KXY = 30°, triangle WKY has angles 65°, 65°, and 30° respectively. 5. **Interpret angle WXY based on K's angles:** - Since K lies inside the rhombus and angles around X add up regarding the triangle formed, angle WXY = 115° matches the rhombus property. 6. **Determine angle VWY if V is a vertex or point on segment; if V is W, then angle WYZ or WXY is relevant. No mention of V in figure, so cannot determine angle VWY without ambiguity. **Final answers:** - angle WXY = 115° - angle VWY cannot be determined with given data. Hence, $$\angle WXY = 115^\circ$$