To solve the problem involving kite WXYZ, we will use properties of kites and the measures of angles given.
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Understanding the Properties of Kites:
- In a kite, two pairs of adjacent sides are equal. For kite WXYZ, sides WX = XY and WZ = YZ.
- The angles opposite the equal sides are equal. Hence, ∠WXY and ∠WZY are opposite angles with respect to the equal sides WZ and YZ.
- The diagonals of a kite intersect at right angles.
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Given Angles:
- m∠WXY = 104°
- m∠VYZ = 49° (assuming this was a typo, and you meant ∠XYZ, as V isn't identified in the kite)
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Finding m∠WYZ:
- Since the angles in a triangle sum up to 180°, we can find ∠XYZ:
- In triangle XYZ, we know that: \[ m∠XYZ + m∠YZW + m∠WYZ = 180° \]
- Since ∠WXY and ∠YZW are adjacent, the angles at vertex Y (∠XYZ and ∠WYZ) can be determined:
- m∠WYZ = m∠WXY (as the opposite angles should be equal in kites):
- Therefore, \[ m∠WYZ = m∠YZW = 49° \quad (because \ m∠YZW + m∠WZY = 180° - 104°) \]
- Thus, we have: \[ m∠WYZ = 180° - 49° - 104° = 27° \]
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Finding Each Angle:
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a. To find m∠VZY (which is the same as ∠WZY): \[ m∠WZY = 180° - (m∠WXY + m∠WYZ) \ m∠WZY = 180° - (104° + 27°) \ = 49° \]
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b. To find m∠VXW (which is the same as ∠WXY): \[ m∠WXZ = m∠WXY = 104° \]
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c. To find m∠VWZ (which is the same as ∠WZY): \[ m∠VWZ = 27° \ (from what we calculated in point 3, ∠WZY = 27°) \]
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Final Answers:
- a. \(m∠VZY = 49°\)
- b. \(m∠VXW = 104°\)
- c. \(m∠VWZ = 27°\)
This shows all the necessary work and conclusions based on the properties of the kite!