Question

ABCD is a kite and <A equal to <C if <CAD equal to 60 degree and Angle cbd equals to 45°, find​

Answer 1

Answer:

∠BCD = 105°

∠CDA = 60°

Step-by-step explanation:

Consider the point of intersection of the two diagonals as O

In ΔAOD and ΔCOD,

AD = CD (Adjacent sides of kite are equal)

AO = CO (BD bisects AC)

OD = OD (Common)

∴, ΔAOD ≅ ΔCOD

 Hence,

∠CAD = ∠ACD = 60°

Using angle sum property in ΔACD,

∠CAD + ∠ ACD + ∠CDA = 180°

60 + 60 + ∠CDA = 180

∠CDA = 180 - 120

∠CDA = 60°

In ΔAOB and ΔCOB,

AO = CO (BD bisects AC)

OB = OB (Common)

AB = BC (Adjacent sides of kite are equal)

∴, ΔAOB ≅ ΔCOB

Hence,

∠AOB = ∠COB

∠BAO = ∠BCO

Using linear pair property,

∠AOB + ∠COB = 180°

2 * ∠AOB = 180

∠AOB = 90° = ∠COB

Using angle sum property in ΔBOC

∠OBC + ∠COB + ∠BCO = 180

45 + 90 + ∠BCO = 180

∠BCO = 180 - 135

∠BCO = 45°

Therefore,

∠BCD = ∠BCO + ∠DCO

∠BCD = 45 + 60

∠BCD = 105°