In the figure, ABCD is a rhombus, whose diagonals meet at O. Find the values of x + y.

Explanation

Since diagonals of a rhombus bisect each other at a right angle.

In  ΔAOB, we have

∠OAB + ∠x + 90° = 180°

∠x = 180° – 90° – 35° = 55°

Also,

∠DAO = ∠BAO = 35°

∠y + ∠DAO + ∠BAO + ∠x = 180°

∠y + 35° + 35° + 55° = 180°

 ∠y = 180° – 125^o = 55°

Hence, the values of x and y are x = 55° and y = 55°.

So , x + y = 110^o 

Final Answer

Thus, the value of x + y is 110°