In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y. -Maths 9th

In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y. -Maths 9th
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Answer :

Since diagonals of a rhombus bisect each other at right angle . ∴ In △AOB , we have  ∠OAB + ∠x + 90° = 180°  ∠x = 180° -  90° - 35° [∵ ∠ OAB = 35°] = 55°  Also, ∠DAO = ∠BAO = 35°   ∴ ∠y + ∠DAO + ∠BAO + ∠x = 180°   ⇒ ∠y + 35° + 35° + 55° =  180°   ⇒ ∠y = 180° - 125° = 55° Hence the values of x and y are x =  55°, y =  55°.       
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