A kite

ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.

Correct answer:

x =  40 °
y =  110 °
z =  55 °

Step-by-step explanation:

$$\begin{gathered} OBC=20\text{ ° } \\ OCD=35\text{ ° } \\ OBA=OBC=20\text{ ° } \\ ABC=OBA+OBC=20+20=40\text{ ° } \\ x=ABC=40=40\text{°} \end{gathered}$$

$$\begin{gathered} OAD=OCD=35\text{ ° } \\ ADO=90-OAD=90-35=55\text{ ° } \\ ODC=ADO=55\text{ ° } \\ ADC=ADO+ODC=55+55=110\text{ ° } \\ y=ADC=110=110\text{°} \end{gathered}$$

$$\begin{gathered} BAD=OBA+OAD=20+35=55\text{ ° } \\ z=BAD=55=55\text{°} \end{gathered}$$

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