Question

In the given kite, calculate $x,y$ and $z.$

• A. $x={50}^o$
• B. $y={58}^o$
• C. $z={32}^o$
• D. All of the above

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $x={50}^o$
B $y={58}^o$
C $z={32}^o$
D All of the above

Both pairs of adjacent sides of a kite are equal, therefore,
$AB=AD$ and $BC=CD$
In $\Delta ABD,\angle ABD=\angle ADB={40}^{\circ }$ (isos. $\Delta$ property)
Since the diagonals of a kite intersect at rt. $\angle s,\angle AOB={90}^{\circ }$.
In $\Delta AOB,x=\angle OAB={180}^{\circ }-({90}^{\circ }+{40}^{\circ })$
$={180}^{\circ }-{130}^{\circ }={50}^{\circ }$
In $\Delta BOC,y=\angle OBC={180}^{\circ }-({90}^{\circ }+{32}^{\circ })$
$={180}^{\circ }-{122}^{\circ }={58}^{\circ }$
Diagonals of kite bisect the angles at the vertices
$z={32}^{\circ }$