Question

In kite WXYZ , m∠XWY=47° and m∠ZYW=18° .

What is m∠WZY ?

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Answer 1

115

Explanation:

took the test and got it correct

Answer 2

Answer:
`\angle WZY=115^(\circ)`

Explanation: Since, here WXYZ is a kite where
`\angle XWY=47^(\circ)` and
`\angle ZYW=18^(\circ)`

Thus according to the property of a kite ,

Exactly one pair of opposite angles are equal and The main diagonal bisects a pair of opposite angles.

Therefore, In kite WXYZ ,

`\angle WZY=\angle WXY` -------(1)

And, WY is the angle bisector of kite WXYZ.

So,
`\angle ZWX=2\angle XWY=2* 47^(\circ)=94^(\circ)` ( because WY bisects
`\angle ZWX` into two equal angles
`\angle XWY` and
`\angle ZWY`)

⇒
`\angle ZWX=94^(\circ)` -----(2)

Similarly,
`\angle XYZ=2\angle ZYW=2* 18^(\circ)=36^(\circ)`

⇒
`\angle XYZ=36^(\circ)` -----(3)

Since, WXYZ is a kite ⇒
`\angle WXY+\angle XYZ+\angle WZY+\angle ZWX=360^(\circ)` -------(4)

Therefore, From equation (1), (2), (3) and (4),

We get,
`\angle WZY=115^(\circ)`