Question

ABCD is a rhombus with angle ABC=40°. find the measurement of angle ACD​

Answer 1

Step-by-step explanation:

Given ABCD is a rhombus.

Diagonals bisect each other perpendicularly. 

Hence ∠BOC = 90°

Given ∠OCB = 40°  

AD||BC and BD is the transversal

∴ ∠ADB = ∠DBC (Alternate angles)

 Hence in right angled DBOC,

 ∠BOC + ∠OCB + ∠OBC = 180° 

⇒ 90° + 40° + ∠OBC = 180° 

⇒130° + ∠OBC = 180° 

⇒ ∠OBC = 180° - 130° = 50° 

But ∠OBC = ∠DBC 

Therefore, ∠ADB = 50°