Question

ABCD is a kite and angle a=angle C if angle CAD=70angle CBD=65 find angle BCD , angle ADC​

Answer 1

Answer:

Given that ABCD is a kite and ∠A=∠C . If angle CAD =70°, ∠CBD=65°

we have to find the measure of ∠BCD and ∠ADC

∠7=70°, ∠6=65°   (given)

By the properties of kite, AB=BC and AD=DC which implies

∠1=∠8 and ∠2=∠7

In ΔOCB, by angle sum property

∠1+∠6+∠BOC=180°

∠1+65+90=180

∠1=25°

In ΔAOD, by angle sum property

∠3+∠7+∠AOD=180°

∠3+70+90=180

∠3=20°

∠1=∠8=25°

∠3=∠5=20°

∠4=90-∠2=90-70=20°

∠BCD=∠1+∠2=25+70=95°

∠ADC=∠3+∠4=20+20=40°