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In the figure given below, ABCD is a rhombus such that $∠ O A B = 35 °$ . Then find the value of y.

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35°

110°

65°

45°

answer is B.

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Detailed Solution

Given is the rhombus ABCD such that

∠ O A B = 35 °

.
We know that diagonals of a rectangle are congruent and bisect each other.
Therefore, in

Δ AOB

,
OA = OB.
Here,

Δ AOB

is an isosceles triangle and therefore base angles will be equal.

∠ O A B = ∠ O B A = 35 °

Now, in

Δ AOB

In the rhombus,

∠ A O B

and y are vertically opposite angles.
Hence,

∠ A O B = y

.
So, the value of y is 110°.
Option 2 is the correct choice.

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