Question

ABCD is a rhombus such that $\angle ACB={50}^{\circ }$. Then, $\angle ADB=$ ?

(a) ${40}^{\circ }$

(b) ${25}^{\circ }$

(c) ${65}^{\circ }$

(d) ${130}^{\circ }$

Answer 1

AD | | BC ∴ ∠CAD = ∠ACB = 50° [alt . int. ∠S]

∵ The diagonals of a rhombus are at right angle to each other .

∴ ∠AOD = 90°

Now , in △AOD , we have

∠ADO + ∠DAO + ∠AOD = 180°

⇒ ∠ADO + 50° + 90° = 180°

⇒ ∠ADO + 140° = 180°

⇒ ∠ADO or ∠ADB = 40°
option a is correct