If ABCD is a kite how can I find angle C, when consecutive sides are congruent? (DA=AB, DC=CB)?

Favorite Answer

Join DB
ADB forms isosceles triangle with AD ≅ AB 
m∠ADB = m∠ABD ... (1)
In Δ ADB,
m∠ADB + m∠ABD + m∠A = 180°

from (1)
 m∠ADB + m∠ADB  +  120° = 180°
2m∠ADB  = 60°
m∠ADB = 30°

m∠ADC =  m∠ADB +  m∠BDC
85° = 30° + m∠BDC
m∠BDC = 55°

Since DC ≅ BC
m∠DBC = 55°

In Δ DBC,
m∠BDC + m∠DBC + m∠C = 180°
55° +  55° + m∠C = 180°
m∠C = 70°...Show more