Question

In
kite WXYZ, m∠ZWY=43°and m∠XYW=12°.
 
What is m∠WXY?


Enter your answer in the box.



photo:

Answer 1

Answer: $\angle WXY=125^{\circ}$

Explanation: Since, a kite has one pair of congruent angles and its main diagonal bisects its opposite angles.

Therefore, According to the given figure,

$\angle WXY=\angle WZY$

And, WY is the main diagonal which bisects angles ZWX and XYZ.

So, $\angle ZWX =2\times \angle ZWY= 2\times 43^{\circ}=86^{\circ}$

And, $\angle XYZ =2\times \angle XYW= 2\times 12^{\circ}=24^{\circ}$

Since, Sum of all angles of a quadrilateral is equal to $360^{\circ}$

Therefore, $\angle WXY+\angle WZY+\angle XYZ+\angle ZWX=360^{\circ}$

⇒$2\times \angle WXY+ 86^{\circ}+24^{\circ}=360^{\circ}$

⇒$2\times \angle WXY=360^{\circ}-110^{\circ}=250{\circ}$

⇒ $\angle WXY=125^{\circ}$